but for some reason this giveaway still appears in my home page

That'll happen for any content which includes at least one DLC, since the Steam developer API (which is what Steam Community websites use) doesn't send any ownership information out on DLC content. Always gotta manually remove those- though, since SG can cross-reference against past win records, SG can at least block users out from entering on anything they've previously won (and marked as Received).

There's also a half dozen other reasons it could happen, but the only other common reasons are 1: that the game is Profile Features Limited (ie, not enough reviews on the game for Valve's anti-exploitation system to acknowledge it as a fully registered game) and 2: the game having been removed from Steam, which also blocks proper ownership recognition- though this is thanks to a certain deliberate change by Valve, with said change also preventing removed games from being listed on your Steam Wishlist, as they were able to be in the past.

tl;dr version: Always expect to have to manually hide any game that is removed from Steam, has at least one DLC, or is labeled on Steam as being Profile Features Limited.

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+1 xD

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me too

same