How can I make already owned games not appear on the giveaway list?

SG + plugin filter.

you can filter it using steam plus plugin for your browser

its because on steam you have Alan Wake and Alan Wake Nightmare, but on SG appears Alan Wake Collector edition...

SG is often not able to determine if you have all items in a pack. In the case of Alan Wake the Collector's Edition is the one being given away and Steam only report yours as Alan Wake. The only way to filter them out is by using Steamgift Plus and adding manual filters.

Alan Wake appears because the giveaways show up as collector's edition but Steam doesnt designate it as such in your library so when SG scans your library it recognizes the game as standard edition and therefore doesnt filter it.

In short, use SG Plus and filter it yourself.

sg+

SG+.

SG+ addon