Its been a while since i last done anything on immunology. I'll do my best to answer your question.
Firstly, Memory B cell recognise antigens upon 2ry exposure, they produce a specific response in which case they proliferate the growth of antibodies that are specific to the antigens found in the infection.
Whilst, T cells are also involved in the 2ry response, however, they do not proliferate the growth of antibodies in a specific manner. They are more to do with enhancing non-specific cells such as activate killer/cytotoxic t cells to kill the ALREADY INFECTED cells?
I hope this helps.