The phrase "hadst hand in" is usually used to describe someone's involvement or contribution to a particular situation or activity. However, if we were to search for antonyms for this phrase, we could consider words like "uninvolved," "disconnected," "withdrawn," or "removed." These words suggest a lack of interaction or engagement with a particular situation, which is the opposite of having a hand in it. In contrast, synonyms for "hadst hand in" could include "contributed," "partook," "participated," or "played a role," all of which suggest a certain level of involvement or engagement.