What do you call a past participle+noun construction clause such as “No offense meant” “Your point taken,” “With that said,” and “Given that”?
These are of a number of types, but what they all have in common is that predictable chunks of a sentence have been left out because they are predictable (to native speakers).
In order, with something like the deleted material in boldface:
No offense meant/taken. = No offense was meant (or taken) by what I (or you) just said.
Point taken. = I have heard and understood the point of what you just said.
- That said, = Now that that has been said, let me continue in a different vein.
- Given that, = Given that topic we just mentioned,
There is no general term for rules that do this, like To be-Deletion, Whiz Deletion, Conjunction Reduction, Conversational Deletion, etc. They are deletion rules, obviously, but far from the only ones.