JLPT N3. Slightly informal. Used mainly in conversation.
We have already covered the grammar for this phrase and the usage can be understood with a direct translation because we have similar expressions in English. The phrase is used to caveat a fact that you state in the prior clause.
I say he’s a CEO, but the company only has three employees.
I say he can speak Japanese, but he cannot yet read or write kanji.
Note that in most cases we can form the same expression just by using “but” as a conjunction; but といっても has nuance that you are qualifying the prior statement rather than contradicting it.