Immunotherapy With E6 T Cell Receptor (TCR) T Cells for Vulvar High-Grade Squamous Intraepithelial Lesions

* INCLUSION CRITERIA: 1. Patients must have vulvar High-Grade Squamous Intraepithelial Lesions (HSIL) as confirmed by pathology report from a Clinical Laboratory Improvement Amendments (CLIA)-certified laboratory. 2. Vulvar HSIL must be human papilloma virus (HPV)-16+ by a polymerase chain reaction (PCR), ribonucleic acid (RNA), or in situ hybridization test from a CLIA certified laboratory. 3. Patients must have measurable lesion(s) as defined in section 6.3.2 and one or more of the following criteria: 1. Failure of surgery to control disease (i.e. positive margins or recurrence of HSIL after surgery). 2. Multifocal or extensive disease for which surgery would result in major deformity that is not be acceptable to the patient. 3. Disease for which surgery would have a risk of functional impairment that is not be acceptable to the patient (i.e. involve partial or complete excision of the clitoris, anus, vagina, or urethra). 4. Patients may have received any previous therapy, including surgical excision, but must have histologically documented recurrence on new biopsy and a measurable lesion that meets the above criteria. 5. The presence of disease that can be biopsied for research purposes is not an inclusion criterion. 6. Patients must have the human leukocyte antigen (HLA)-A\*02:01 allele 7. Age greater than or equal to 18 years and less than or equal to 65 years. As age increases, the ability to tolerate the toxicities of aldesleukin decreases, so the patient population for this study will include up to and including 60 years of age to increase safety. 8. Eastern Cooperative Oncology Group (ECOG) performance status of 0-1. Able to understand and sign the Informed Consent Document. 9. Women of child-bearing potential must have a negative pregnancy test. Women of child-bearing potential are defined as all women who are not post-menopausal or who have not had a hysterectomy. Postmenopausal will be defined as women over the age of 55 who have not had a menstrual period in at least 1 year. 10. The effects of E6 T Cell Receptor (TCR) T Cells on the developing human fetus are unknown. For this reason, women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she is participating in this study, she should inform her treating physician immediately. 11. Seronegative for human immunodeficiency virus (HIV) antibody. The experimental treatment being evaluated in this protocol depends on an intact immune system. Patients who are HIV seropositive can have decreased immune-competence and thus be less responsive to the experimental treatment. 12. Seronegative for hepatitis B antigen and hepatitis C antibody. If hepatitis C antibody test is positive, then the patient must be tested for the presence of antigen by reverse transcription (RT)-PCR and be hepatitis C virus (HCV) RNA negative. 13. Must be willing to participate in Gene Therapy Long Term Followup Protocol (15-C-0141), which will follow patients for up to 15 years per Food and Drug Administration (FDA) requirements. 14. Patients must have normal organ and marrow function as defined below: * leukocytes greater than or equal to 3,000/mcL * absolute neutrophil count greater than or equal to 1,000/mcL * platelets greater than or equal to 150,000/mcL * hemoglobin greater than or equal to 10.0 g/dL * total bilirubin within normal institutional limits except in patients with Gilbert's Syndrome who must have a total bilirubin \< 3.0 mg/dL * Aspartate aminotransferase (AST) serum glutamic-oxaloacetic transaminase (SGOT)/alanine aminotransferase (ALT) serum glutamic pyruvic transaminase (SGPT) Serum ALT/AST \< 3 times ULN * creatinine less than 1.5 times baseline, \< 1.5 times upper limit of normal (ULN) OR -creatinine clearance less than or equal to 60 mL/min/1.73 m(2) for patients with creatinine levels above institutional normal (by the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation) EXCLUSION CRITERIA: 1. Patients who are receiving any other investigational agents 2. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with E6 TCR, breastfeeding should be discontinued if the mother is treated with E6 TCR. These potential risks may also apply to other agents used in this study. 3. Uncontrolled intercurrent illness including, but not limited to, any ongoing or active infection (e.g. requiring anti-infective therapy), coagulation disorders, cardiovascular disorders, respiratory disorders, cancer, or psychiatric illness/social situations (within the last six months) that would limit compliance with study requirements. 4. Any form of systemic immunodeficiency, including acquired deficiency such as HIV or primary immunodeficiency such as Severe Combined Immunodeficiency Disease. The experimental treatment being evaluated in this protocol depends on an intact immune system. Patients who have decreased immune competence may be less responsive to the treatment. 5. Concurrent systemic steroid therapy if greater than the equivalent of 5 mg prednisone by mouth (PO) daily. Patients previously on steroids must be off steroids for four weeks prior to treatment. 6. Any history of clinically significant cardiac arrhythmia, coronary revascularization, ischemic symptoms, or previously documented left ventricular ejection fraction (LVEF) of less than or equal to 45%. A cardiac stress test is required for all patients greater than 50 years old. A cardiac stress test may also be performed for any clinical concern. Patients with cardiac ischemia are not eligible. 7. Patients with any active invasive cancer are not eligible. 8. Patients vulvar HSIL that is not HPV-16+ or is associated with multiple types of high-risk HPV are not eligible.