Doylian answers are boring, so here are two possible watsonian ones:

a) The episode takes place in a universe where Mr. Poopy Butthole exists, whereas in the universe or universes where other episodes take place he does not. The parasite incident still occurred in the timeline(s) of the other episodes, but, because Mr. Poopy Butthole does not exist in said timeline(s), the pillowfight frame in the title sequence of other episodes doesn't have him in it. This is the simplest answer within the rules of the show's multiverse or canon.

b) Mr. Poopy Butthole is actually a trans-dimensional superbeing capable of inserting himself into timelines and the memories of those in said timelines in a similar manner to the parasites. It's possible then that he can also remove himself in a similar fashion. This is primarily supported by the fact that he's the only character besides Rick (another interdimensional wanderer) to break the fourth wall. This could also mean that he's the one who tracked the parasites.

But of course, those are both just theories.