Thank you for your understanding or Thank you for your comprehension?
Thank you for your understanding is the correct phrase.
It means that you are thanking the person, or persons involved for showing sympathy towards your issue. In this case understanding does not mean to grasp something and understand the way it works. It means that a person understands the difficulties you might be having and chooses to acknowledge them.
When you say ‘thank you for your understanding’ you are thanking the person, or persons, involved for being considerate. Because of this changing the word understanding for comprehension is wrong, both grammatically and in terms of theme.
A recruiter once sent me an email ending in “Thank you for your understanding and comprehension.” after I asked for an update when I haven’t heard from them in weeks given that I’ve already submitted a lot of sensitive documents.
It OFFENDED me. Ending with “understanding” might have sufficed but adding “comprehension” is as if implying that I lack comprehension and am impatient when in fact, I have every right to ask for updates because I have already submitted a lot of sensitive documents to the company after they’ve told me that I am supposedly in the final steps.
Yes, that’s not nice when a company acts that way.