Whether or not this interaction is healthy totally depends on the context of the client and the recipient of the action.

This particular client, the OP, analyzes things and reads into things a lot. If the client is constantly hunting for evidence of her own specialness to the T, and wanting proof that T loves her as a daughter, than the T should not act in ways that reinforce that perception.

I wonder if this T is feeling a bit on edge trying to maintain the connection and help the client, while at the same time worrying about each action being fraught with over-identification and too much meaning.

Thanks for sharing the interaction, it is a sweet one but I just worry you'll take it out of context.