Ideally people would check if they had the game or DLC being given away before entering and/or redeeming, but they tend to trust that the system is checking for them. Unfortunately, the system isn't great at detecting owned DLCs. It's an easy mistake to make, and I do appreciate you letting me know.

As far as marking as received goes, the rule is:

When should I mark a gift I won as "Received" or "Not Received"?
You should only mark a gift as "Received" when you have both (i) received the exact game described in the giveaway, and (ii) activated that game on the Steam account you used during registration. In all other instances you should mark the gift as "Not Received" one week after the giveaway has ended.

In this case, the "proper" thing would have probably been to just not mark anything, but I do believe you had good intentions. It can be a bit confusing when you consider these unusual situations.

Marking a giveaway as Received implies that you have received the gift and activated it on your account. Doing so with a gift you already owned results in supension for winning the same game multiple times. Therefore a giveaway should bever be marked as received if the gift is rejected. The giveaway creator has already cited the relevant part of the FAQ.

You can easily check if you already own a title by simply clicking the Steam store link inside the giveaway (i.e. clicking the game icon in the top left corner). If the page shows the large green banner indicating that you already own the game, since when or how long you've played it, it's clear that you do own it and should not reveal the key.

If a game's [DLC's] information is not available in Steams API then there's no way to check for it.
There's other things to consider though: As pointed out by myself and the giveaway creator, the sites rules require you to only enter giveaways for games that you don't own, yet. While I understand that hardly anyone does that and instead simply relies to the site's settings that are just meant to help with that (which has it's limitations as explained above), there are tools that make this a really easy task. For example the Steam Web Integration script.
It shows you a green checkmark besides every Steam Store link for titles that you already own and a red cross if you do not own a title, yet. That way one can directly see if something is already owned or not.
I can only recommend using SWI. Not only to make things easier for oneself in order to follow the rules but also to help avoid unnecessary tickets and thus trouble for yourself and the giveaway creator.

You should hide giveaways for the game so this doesn't happen again.

Have a nice day.