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he didn't remember WHO he did the handshake with, but he still remembered HOW to do the handshake

it's like...I may not remember who taught me to shoot a jump shot but I still remember how to do it (that's a terrible example but hopefully you get my point). In this instance the thing he remembers how to do he only did with one other person. No one else would walk up to him and initiate that handshake and do all of the moves together with him. so while he doesn't know this person beyond their one meeting (to him) something is up with him, and we are to believe that Peter will finally tell him like he told MJ

at least that's how I interpreted it