Its and it's cause more red ink than almost any other pair, and the reason is that English apostrophes usually do mean ownership. The dog's bowl, Sam's coat, the city's parks: apostrophe, then s, then the thing owned. So "it's paw" looks right by analogy. It isn't.

The pronoun it works like the other pronouns, and none of them use an apostrophe to own things: his car, her idea, their house, its paw. Learner's dictionaries list its as a possessive determiner alongside my, your and his. The apostrophe form, it's, is something else entirely: a contraction, with the apostrophe standing in for letters you've squeezed out of it is or it has.

That gives you a test that never fails. Read the sentence aloud with "it is" or "it has" in place of the word. If it still makes sense, write it's. If it turns into nonsense ("the company changed it is name"), write its.

One more trap: its', with the apostrophe after the s, doesn't exist. There are only two spellings, and each has exactly one job.

Memory trick. The apostrophe is a gap where letters fell out. It's has a gap because it is lost its i. Its (possessive) has nothing missing, so it has no gap, the same as his and hers.