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As simple as the title!
You don't need anything else just to vote for this idea and the folks at Spotify give us our power back to control the songs we don't want them to show on the recently played and so...
Updated on 2019-11-02
Hello and thanks for bringing your feedback to the Idea Exchange.
A similar idea has already been suggested here: https://community.spotify.com/t5/Live-Ideas/All-Platforms-Music-Remove-items-from-Recently-Played-hi...
We'd recommend adding your +VOTE and feedback there.
Keep in mind that on the desktop app, you should be able to remove an item from your Recently Played list by tapping the three dots (Mac) or right clicking (Windows) of the item you wany removed.
More information about how the Spotify Idea Exchange works can be found here.