The mouse is "borrowing" bits of cheese and leaving little I.O.U.s ("I Owe You") in the refrigerator. Garfield tells him to stop doing that, and the mouse says "I'm good for it." In other words, the mouse is saying that he will return the cheese he has "borrowed."
If someone owes a debt and says "I'm good for it," he means that he can be depended on to repay the debt in the future.
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