Yes, please. These links really clutter the page, especially for browser games, where they overlap the player window if not maximized. This is becoming a consideration for me over whether to submit existing projects to bundle/showcase type jams, and I have also considered doing as you say and removing certain old submissions. It's noise.
I'm not opposed to the link being present, since it does (slightly) benefit mutual discoverability after the fact, but the placement of it is bad. Maybe the theme editor can provide an option to toggle between the "badge" style and a list of links placed at the bottom of the page above the comment section, where they don't interfere with the actual page content.
Or, another idea could be to have one collapsed "Jam Submissions (3)" badge that the user can click to expand or collapse again. As a user browsing games, I rarely care about what jams a game has been submitted to anyway. I can easily expand the list if I really want to know.
There's also another issue with these links, which is that they remain even when the jam is no longer accessible, like this one:
The user who created this jam is long gone, and the link to the jam is dead. Clicking it generates a 404 error.