In “I called for confirmation that ...”, confirmation is the object, however in “thank you for confirming that ...”, confirming is the verb. The sentence doesn't really work without both unless you want to be curt or efficient and just say "Thanks.", though this requires them to know you're referring to "for the confirmation".
There's no reason you can't use the noun to refer to the past tense, you just have to add in a different gerund as the verb you're performing on the object (confirmation), for example:
Thank you for providing confirmation of your stay at the hotel.
Thank you for sending confirmation of your stay at the hotel.