Option to hide owned games from groups?

If you've activated the option "Hide giveaways for owned games" they won't show up, but that affects all giveaways, not only group... or I misunderstood your question.

no, no way to hide in group, user pages or archive view.

not a regular steamgifts option, but there is a user script that add's the function to block owned & hidden games from group pages.
it is among several different scripts located here inside Daerphen's topic, called sggrouphiding.user.js
there are many other scripts that can be located here (Sighery's SG Add-Ons Registry)