If a therapist gives a very low hourly rate to a financially challenged client do therapists get annoyed when the client is seemingly irritated with the therapist for other reasons: do they think the client should be grateful for cheap consults?

The rate agreed upon is a separate issue. A therapist should only offer a rate he can live with. It would be unfair to tie extra expectations to that rate beyond the standard expectations that the client will pay the rate, show up to sessions and engage in the work.

Once the rate has been agreed to, then therapy must proceed as normal. It’s based on what the needs of the client are. If the client gets irritated with the therapist, then the therapist can notice it and explore those feelings with the client, and work with her to resolve them as the client desires.