Genetically Modified Cells (KIND T Cells) for the Treatment of HLA-A*0201-Positive Patients With H3.3K27M-Mutated Glioma

Eligibility Criteria

• * Participants 3 to 25 years of age inclusive, at the time of signing the informed consent. The first two participants will be 12 years of age or older.
• * Male participants of impregnate potential must agree to use contraception, during the study and for at least 6 months after the last study intervention and refrain from donating sperm during this period.
• * Female participants of childbearing potential must agree to follow the contraceptive guidance, during the study and for at least 6 months after the last study intervention.
• * Females of childbearing potential must have a negative serum or urine pregnancy test within 14 days of receiving study interventions.
• * Central nervous system (CNS) reservoir such as Ommaya catheter must be in place.
• * Newly diagnosed participants with intracranial diffuse midline gliomas (DMG) who are positive for the H3.3K27M mutation (positive testing from a Clinical Laboratory Improvement Amendments (CLIA) laboratory required or equivalent) and who completed standard radiation therapy.
• * Participants that have received any tumor directed therapy other than radiation must be discussed with study chairs.
• * All participants must t test positive for HLA-A\*0201 (positive testing from a CLIA or equivalent laboratory required). Other HLA-A2 subtypes are excluded.
• * All participants must consent for tumor tissue (fresh or archival) for biomarker analysis.
• * All participants must have measurable disease at the time of consent.
• * All participants must be either off systemic steroids or be on a stable dose of dexamethasone (maximum dose of 0.1 mg/kg/day or 4 mg/day) at the time of enrollment.
• * All participants must be off systemic steroids for 7 days or more prior to leukapheresis.
• * Participants must not have received any bone marrow transplants for the treatment of their tumor.
• * All participants must have started standard radiation therapy within 6 weeks of diagnosis by either imaging or tissue confirmation whichever was completed last (biopsy or surgery).
• * Peripheral absolute neutrophil account 1000/mm\^3
• * Platelet count 100,000/mm\^3 (transfusion dependent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment)
• * Absolute lymphocyte count \>= 500/microliter (uL) or cluster of differentiation 3 (CD3) count of \>= 150/uL
• * Creatinine clearance or radioisotope glomerular filtration rate \>= 70 mL/min/1.73 m\^2 or maximum serum creatinine based on age/gender as follows:
• * 3 to \< 6 years =\< 0.8 mg/dL (male and female)
• * 6 to \< 10 years =\< 1.0 mg/dL (male and female)
• * 10 to \< 13 years =\< 1.2 mg/dL (male and female)
• * 13 to \< 16 years =\< 1.5 mg/dL (male) and 1.4 mg/dL (female)
• * \>= 16 years =\< 1.7 mg/dL (male) and 1.4 mg/dL (female)
• * Bilirubin (sum of conjugated + unconjugated) =\< 1.5 x upper limit of normal (ULN) for age
• * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2.5 x ULN
• * Serum albumin \>= 2 g/dL
• * Corrected QT interval (QTc) =\< 480 ms
• * Shortening fraction \>= 27% by echocardiogram
• * No evidence of dyspnea at rest
• * No exercise intolerance due to pulmonary insufficiency
• * Pulse oximetry \> 92% while breathing room air
• * A well-controlled seizure disorder
• * Performance status (Lansky \< 16 years and Karnofsky \>= 16 years) that is at least 70
• * Capable of giving signed informed consent or assent depending on participant age as appropriate which includes compliance with the requirements and restrictions listed in the informed consent form (ICF) and in this protocol. Assent will be obtained when appropriate based on the subjects age.
• * Participants with magnetic resonance imaging (MRI) or clinical evidence of uncontrolled tumor mass effect; the assessment of mass effect should be made by the study investigators prior to any planned KIND T cell treatment. Pre-infusions MRI will need to be reviewed by the study investigators prior to dosing. Participant with an assessment score \>= 3 will be excluded
• * Participants with DMG located in the spinal cord
• * Participants with a known disorder that affects their immune system such as human immunodeficiency virus (HIV) or hepatitis B or C, or an autoimmune disorder requiring systemic cytotoxic or immunosuppressive therapy. Participants who are currently using inhaled, intranasal, ocular, topical, or other non-oral or non-IV steroids are not necessarily excluded from the study.
• * Participants who have received prior solid organ or bone marrow transplantation.
• * Participants with uncontrolled infection.
• * Female participants of childbearing potential must not be pregnant or breast-feeding.
• * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection,symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
• * Untreated symptomatic hydrocephalus determined by treating physician.
• * Participants who are unable to return for follow-up visits or obtain follow-up studies required to assess toxicity to therapy.
• * Participants who are currently receiving another investigational drug.
• * Participants who are currently receiving other anticancer agents (bevacizumab used to treat tumor mass effect will not constitute an exclusion; at time of enrollment participants need to be off bevacizumab and will need to be discussed with the study team).