What sort of files are they? You should be able to remove the tilesets from your map and remove that error for tilesets. For object templates, I think you’ll need to either remove the objects using them or replace their properties with manually set ones.
If the fact that they don’t load is preventing you from removing them, you can remove references to them in the TMX itself using a text editor.
In the future, you should first remove any usages of files in Tiled before you delete the files entirely, to give Tiled an opportunity to do any clean-up it needs. The missing files feature isn’t designed to handle deletions as far as I can tell, but those cases where files get moved or where the directory structure changes, which is why Ignore just keeps the references as is.