OK, so not grammar -- you CAN toss a dead cat in someone's backyard, but I think the intended meaning is "toss that dead cat INTO someone else's backyard", because she clearly means that she would be happy to get rid of an employee she doesn't want -- Dilbert.
Yes, I know that it is somewhat pedantic to correct grammar in a comic strip, but to get the intended meaning across, or in this case, for the joke to work, the correct words have to be used.
If you are pedantic enough to complain about grammar in a comic strip (and do not construe that I suggest it to be a bad thing), you might try to get it right. Tossing a dead cat IN someone's backyard is perfecty feasible - both syntax and semantics are accurate, as far as panel 2 is concerned. Not convinced? Enter the backyard of another with a cat, ensure it is dead at time of tossing, and perform said act. You would then be "tossing that dead cat in someone else's backyard". Ah, but does it make sense, you ask? Does tossing cats, dead or alive? It's the author's opinion. And, oh, it is a comic strip.
Dilbert's too used to PHB who won't let him transfer to a better job (and a better boss) because he's too "valueable", then assigns him a pointless assignment. In this one they can't wait to get rid of him. I'm not sure which is worse.