“... don’t have antibodies 17 years later/ They have memory T-Cells with record of the virus.”
Antibodies are expressed on the surface of the memory cells. They proliferate when encountering the antigen.
Soluble antibodies probably are present but too low to detect.
No, that's not how that works at all. Antibodies are not produced by T-cell lymphocytes. They're produced by B-cell lymphocytes.
You've got the wrong cells.