You have to be really ignorant and not paying attention to think cp 0 had nothing to do with a meeting that was set up specifically to sell children to them. It want a fun party for no reason. There is another party present in the scene we never witnessed.
So I'm the ignorant because I'm understanding what Oda wrote without making up some boring headcanon about CP0 agents doing something you can't even imagine properly because the author gave literally zero hints to infere it, and said something would be so, so terrible that the giants (a tribe of warriors whose crew terrified the whole world) weren't able to pronounce Linlin's name (specifically) anymore (for THAT reason and not for killing one of their war heroes), so messed-up that had Streusen laughing his ass off yet being scared by Linlin approaching him, so strange that erased from existence any trace of an hypothetical battle involing CP and only left two witnesses of whatever happened then (two, as stated by the narrator)?
And, on top of that, we have the context of Linlin eating so uncontrollably that she can't even see what she's doing and she enters a mental state similar to her tantrums, Carmel's clothes nibbled (I'm sorry: ripped with a perfect pattern that directly reminds of bites like those of Linlin's teeth), screams above the island as Linlin eats (and before she finishes her meal), the table and chairs completely destroyed...
Just do the math.