[verb た-form] + ところで
たところで means "even if you did, it would be no use": the action wouldn't change anything. It follows the た-form of a verb, and the second half says the result won't come, is pointless or is too late.
The た-form doesn't make it past: the action is imagined and hasn't happened. いくら, どんなに and いまさら今さら often come before it to stress how pointless it would be.
たところで belongs to writing and to a resigned or argumentative tone in speech. The everyday way to say the same is きごう〜てもむだ無駄だ or きごう〜てもいみがない意味がない.
Because the result is a judgement about something that hasn't happened, the second half doesn't report a past event. For that, use ても.
These go beyond "it would be no use".
With せいぜい or たかが, the second half says the outcome would be small: "even if it happened, it'd only be…".
The same words can also mean "at the point when" an action finishes. Then the second half is what happened next, and the sentence can be past.