The red sometimes (very often) doesn't dissapear if you look at the new items with the "just new" filter. If you scroll through your artifact list without filter and klick on the artifacts with red dot, it should dissapear. It's best to do immediately after using the "just new" filter, so you know in wich sets you have to search for new artifacts and don't have to scroll the whole list.

Here's how to get rid of that evil dot, from one of our Discord Mods:

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Thanks very much - I found two items that way and it's finally gone 👍

Yay!