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 โthank you for your understandingโ 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 โThank you for your understanding and comprehension.โ after I asked for an update when I havenโt heard from them in weeks given that Iโve already submitted a lot of sensitive documents.
It OFFENDED me. Ending with โunderstandingโ might have sufficed but adding โcomprehensionโ 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 theyโve told me that I am supposedly in the final steps.
Yes, thatโs not nice when a company acts that way.