A Study to Compare T-Guard vs Ruxolitinib for Treatment of Steroid-Refractory Acute Graft-vs-Host Disease (BMT CTN 2002)

Inclusion Criteria: To be eligible to participate in this study, patients must meet the following: 1. Patients must be at least 18.0 years of age at the time of consent. 2. Patient has undergone first allo-HSCT from any donor source or graft source. Recipients of nonmyeloablative, reduced intensity, and myeloablative conditioning regimens are eligible. 3. Patients diagnosed with Grade III/IV SR-aGVHD after allo-HSCT. SR includes aGVHD initially treated at a lower steroid dose, but must meet one of the following criteria: * Progressed or new organ involvement after 3 days of treatment with methylprednisolone (or equivalent) of greater than or equal to 2 mg/kg/day * No improvement after 7 days of primary treatment with methylprednisolone (or equivalent) of greater than or equal to 2mg/kg/day * Patients with visceral (GI and/or liver) plus skin aGVHD at methylprednisolone (or equivalent) initiation with improvement in skin GVHD without any improvement in visceral GVHD after 7 days of primary treatment with methylprednisolone (or equivalent) of greater than or equal to 2mg/kg/day * Patients who have skin GVHD alone and develop visceral aGVHD during treatment with methylprednisolone (or equivalent) of greater than or equal to 1mg/kg/day and do not improve after 3 days of greater than or equal to 2mg/kg/day Improvement or progression in organs is determined by comparing current organ staging to staging at initiation of methylprednisolone (or equivalent) treatment. 4. Patients must have evidence of myeloid engraftment (e.g., absolute neutrophil count greater than or equal to 0.5 × 109/L for 3 consecutive days if ablative therapy was previously used). Use of growth factor supplementation is allowed. 5. Patients or an impartial witness (in case the patient is capable of providing verbal consent but not capable of signing the informed consent form (ICF)) should have given written informed consent. Exclusion Criteria: Patients will be excluded from study entry if they meet any of the following exclusion criteria: 1. Patients who have a creatinine greater than or equal to 2mg/dL or estimated creatinine clearance less than 40 mL/min or those requiring hemodialysis. 2. Patients who have been diagnosed with active thrombotic microangiopathy (TMA), defined as meeting all the following criteria: * Greater than 4% schistocytes in blood (or equivalent if semiquantitative scale is used e.g., 3+ or 4+ schistocytes on peripheral blood smear) * De novo, prolonged or progressive thrombocytopenia (platelet count less than 50 x 109/L or 50% or greater reduction from previous counts) * Sudden and persistent increase in lactate dehydrogenase concentration greater than 2x the upper level of normal (ULN) * Decrease in hemoglobin concentration or increased transfusion requirement attributed to Coombs-negative hemolysis * Decrease in serum haptoglobin 3. Patients who have previously received treatment with eculizumab. 4. Patients who have previously received checkpoint inhibitors (either before or after allo-HCT). 5. Patients who have been diagnosed with overlap syndrome, that is, with any concurrent features of cGVHD. 6. Patients requiring mechanical ventilation or vasopressor support. 7. Patients who have received any systemic treatment, besides steroids, as upfront treatment of aGVHD or as treatment for SR-aGVHD. Reinstitution of previously used GVHD prophylaxis agents (e.g., tacrolimus, cyclosporin, methotrexate \[MTX\], MMF) or substitutes in cases with previously documented intolerance will be permitted. Previous treatment with a janus kinase (JAK) inhibitor as part of GVHD prophylaxis or treatment is not allowed. 8. Patients who have severe hypoalbuminemia, with an albumin of less than or equal to 1 g/dl. 9. Patients who have a creatine kinase (CK) level of greater than 5 times the upper limit of normal. 10. Patients with uncontrolled infections. Infections are considered controlled if appropriate therapy has been instituted and, at the time of enrollment, no signs of progression are present. Persisting fever without other signs or symptoms will not be interpreted as progressing infection. Progression of infection is defined as: * hemodynamic instability attributable to sepsis OR * new symptoms attributable to infection OR * worsening physical signs attributable to infection OR * worsening radiographic findings attributable to infection Patients with radiographic findings attributable to infection within 4 weeks prior to enrollment must have a repeat radiographic exam within one week of enrollment that documents absence of worsening. 11. Patients with evidence of relapsed, progressing, or persistent malignancy, or who have been treated for relapse after transplant, or who may require rapid immune suppression withdrawal as pre-emergent treatment of early malignancy relapse. 12. Patients with evidence of minimal residual disease requiring withdrawal of systemic immune suppression. 13. Patients with unresolved serious toxicity or complications (other than aGVHD) due to previous transplant. 14. History of sinusoidal obstruction syndrome (SOS)/veno-occlusive disease (VOD). 15. Patients with known hypersensitivity to any of the components murine monoclonal antibodies (mAb) or Recombinant Ricin Toxin A-chain (RTA). 16. Patients who have had treatment with any other investigational agent, device, or procedure within 21 days (or 5 half-lives, whichever is greater) prior to enrollment. An investigational agent is defined as medications without any known FDA or European Medicines Agency (EMA) approved indications. 17. Patients who have received more than one allo-HSCT. 18. Patients with known human immunodeficiency virus infection. 19. Patients who have a BMI greater than or equal to 35 kg/m2. 20. Patients who are taking sirolimus must discontinue prior to starting study treatment. The sirolimus blood level must be less than 2 ng/mL prior to starting study treatment. 21. Female patients who are pregnant, breast feeding, or, if sexually active and of childbearing potential, unwilling to use effective birth control from start of treatment until 30 days after the last study treatment. 22. Male patients who are, if sexually active and with a female partner of childbearing potential, unwilling to use effective birth control from start of treatment until 65 days after the last study treatment. 23. Patients with any condition that would, in the investigator's judgment, interfere with full participation in the study, including administration of study drug and attending required study visits; pose a significant risk to the patient; or interfere with interpretation of study data. 24. Patients whose decision to participate might be unduly influenced by perceived expectation of gain or harm by participation, such as patients in detention due to official or legal order.