When it comes to deleting items from APIs, first you need to make sure the API has a DELETE endpoint. Usually public APIs, like the one you have, don’t. They only allow you access the data. I’d suggest trying that with Supabase or Xano and then updating the data using plugin actions.
You could copy the API response to a separate array or object variable and then bind your quotes to that variable instead. Then you can either remove the quote from the variable after clicking the X or adding a true/false value in your variable to hide the quote, but keep the quote in the variable.