Your task [ is to / is ] remove all the dirt.
All I want to do [ is to / is ] thank you.
Between “is to” and just “is“, what is more common, and what’s the difference in their meaning or usage.
In the first sentence, the subordinator “to” is obligatory. The version without “to” would be ungrammatical, at least in the standard English.
The “to” in the second sentence, however, is optional because there’s a form of “do” in the relative clause that modifies “all”. This is addressed in Huddleston & Pullum’s (2002) The Cambridge Grammar of The English Language, where they claim a bare-infinitival clause can function as a predicative complement when the subject NP is modified by a relative clause that contains the verb “do”:
ii. All I did was print out the table of contents. [bare infinitival]
The bare-infinitival is restricted to cases where the subject NP contains do in a relative clause; as we have noted, to can be added here (All I did was to print out …).