I agree with Okada-san, but here is a bit of explanation.

This is a classical Japanese construction. すれ is the 已然形 of する. The 已然形 was used in classical Japanese to show that an action had been completed. You add ども to the 已然形 to express 逆接の確定条件, or a condition that has already happened acting as a contradictory conjunction (i.e. past tense + but). So in your example it means したけれども.

If this were actually classical Japanese, this construction could technically also be translated (into modern Japanese) as しても, but when you see classical constructions thrown into modern Japanese like this it's usually just for style and will be used in the most easily understood (most obvious) meaning.

By the way, in modern Japanese grammar the 已然形 is often referred to as the 仮定形 because it's pretty much only used in the ば (hypothetical) conditional construction.