Anakin wouldn't believe there wasn't mutual studying going on, Anakin studying Garth'zel intently and Garth'zel studying him just as much. General life experience told Anakin it didn't actually matter if Garth'zel was pissed off with him or not - he was close and had no recourse to fight back. Experience with Garth'zel said he wasn't the type to take his temper out on Anakin. The latter wins out, even if only barely. With time, Anakin would trust that more - he just needed time. "Ok." He could do that even if he wasn't going to be relaxed.

Not everyone waited for permission, but he was dressed better at least. That would be some protection.