Since this (#147) isn't possible, maybe there could be an option to quickly hide specific groups from the dungeon finder. This could be done, for example, by rightclicking the group or some combination like ctrl + rightclick. It can be quick to determine if you don't want to join a group just by looking at it, like when it isn't an upgrade for you.
There could probably also be an option to reset these hidden groups.

Not a bad idea, removal could be temporary (does not match) or permanent (WTS/spam groups). However I wonder if the issue could just be solved with a key level filter in the search box.

Of course you might have very different ratings for individual dungeons, but isn't there always a key level where you feel comfortable that you would type into the search box? Let's say your best is Algethar +15 and Shadowmoon +18. I claim that you would not search for +16 and "click-remove" Shadowmoon +16. I think you would simply search for +18 as that's what's possible for you and provides the best loot.

A problem with this idea is that it would require quite some rewrite of the code, similar to #154. Currently groups are only removed when the list is fetched from the server. Once the list is displayed, PGF does not change it anymore. Another minor issue is that groups do not have a unique ID. So the best identification is the group leader's name, which is not immediately available.