Neutrophils do not have memory of any pathogen. They attack any pathogen indiscriminately, not selectively. This is why they belong to the innate (non-specific) arm of the immune system.
Memory T- cells are lymphocytes that are specifically produced and act against pathogens that were encountered at least at one time before. The memory of that encounter is kept and when the same kind of pathogen is encountered a second time, it is remembered by these cells and they very specifically single it out and destroy it. These cells belong to the specific or adaptive arm of the immune system.
