Mr. Meeseeks can only die when he has fulfilled your wish, and pain is existence for them. Summer is the granddaughter of Rick and the sister of Morty. Rick invented/found the Meeseeks and Morty decided he wanted to fix the world with them or something. I can't really remember, or remember who Tammy* is.
"Tammy Gutermann is a deep-cover agent for the Galactic Federation, and the daughter of Pat Gueterman and Donna Gueterman."
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So I think Tammy basically checks that illegal travel and messing with the universes doesn't happen - which is basically Rick's go-to-thing "oh shit we fucked up this universe OK let's leave and go find another one where the other we's are dead" and he is wanted by them. Summer's use of the Meeseeks thus outed a connection to Rick, a highly wanted man.
Kills BirdPerson and ruins Rick's attempt to fix his life
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So I think Tammy basically checks that illegal travel and messing with the universes doesn't happen - which is basically Rick's go-to-thing "oh shit we fucked up this universe OK let's leave and go find another one where the other we's are dead" and he is wanted by them. Summer's use of the Meeseeks thus outed a connection to Rick, a highly wanted man.
Y’alls comments were helpful too