[His explorations will find that there is in fact a cat sitting right there. In order to have weight, Chessur has to stop being intangible, even if the invisibility is another thing entirely. It's certainly true that he doesn't always leave one of the two aside, but well. He might as well for a moment or three, given the circumstances.]

Then it's hardly strange.

[Inconvenient, yes. But not actually strange.]