@Lydia_Pintscher, we have an incoming volunteer patch for this. Can you please decide on how to proceed here? It's a little more complicated because removing this unwanted "feature" does have implications we need to think about. E.g. what should happen to empty sitelinks when you can not remove them with the backspace key any more? I think we need to track this properly in our sprint and invest some time to get this right.
Change 370808 abandoned by Thiemo Kreuz (WMDE):
[WIP] Restore add and remove feature in the sitelink UI
I, personally, don't have time to continue working on this. I wish the Wikidata team would pick this up. But it's more likely this issue will exist until the UI got redone.