'그렇다 해도 무지하게 반겨 주잖아' => Even then, don't they're welcoming you like crazy. => Be that as it may, they're going overboard welcoming you. The sentence has both the subject and the object omitted, so all we know is someone or some animal(s) is greeting someone else or some other animal with great enthusiasm. It also sounds a little odd because it uses 무지하게 about welcoming someone, as the word has a somewhat negative connotation, like "insanely" for example. - 그렇다 해도 = 그렇다고 (인정)해도 = even if we take/accept that as such / be that as it may / even then. - 무지하게 = adverb form of 무지하다 = 1) be ignorant, 2) very much; to an unreasonable extent. - 반겨 주잖아 = 반겨 주다(greet with a welcome) + -잖아 (-지 않아). - X-잖아 = rhetorical question to stress 'X이다' = It is X (asks the opposite 'X-지 않아?' to stress a point). For example, '좋잖아' means 좋아 but it's more natural and effective, in the same way "Boy, am I hungry!" sounds more emphatic than "I am hungry".