Is there a difference between removal of a game and uninstalling.

Uninstall of a game: You remove the software of your PC, but can install it again later;
Removal of a game: You remove the licence of your Steam [In this case] account, and can't use unless you buy it again.

You can completely remove a game from steam, but its not the same as uninstalling, that is perfectly fine.
Noone has a game installed when they first get it anyway, wouldn't make sense for people with 2000+ games.

Uninstalling a game is no problem for SteamGifts. SteamGifts checks what's in your game library.

When people talk about removing games of their library, they are talking about the process of contacting Valve support to have a game completely removed from their Steam game library.

You actually can freely re-add games after you've removed them. However, while they're removed, they however are no longer actively associated with your account, meaning that Steam no longer recognizes you as owning the game for its interactions. As such, it means you can repurchase/reactivate a new copy of the game [which is useful if you want to try installing a different language version of the game], but also that SG will flag your account for Non-Activations.

If you do happen to decide that you want to remove a SG win from your account, contact the GA creator and ask if they'd be agreeable to deleting the giveaway- if you provide them with a trade of games of higher CV value than the game you want deleted, many GA creators will likely agree to the request.
Otherwise, to avoid issues of accidental repurchase and SG flagging, your best option is simply to hide completed/no-longer-desired games by clicking the 'Hide this game' checkbox in the bottom left of the categories tab for that game (accessed by right-clicking on the game).

thanks all for the lightening quick replies o/ good to know :)