Got it... the "ID" is just a column name, apologies for not explaining that better. You'd use there the name of whatever your main identifier column is, maybe "Title" or whatever it would be.
If you add a button for testing, to pull the data into a collection you would use this on the OnSelect property:
ClearCollect(colTest,'Travel Reimbursements')
or something like that. colTest would be the name of the collection, and 'Travel Reimbursements' is your data source. After pressing the button, you can go to "Collections" to see the first 5 items and confirm it worked.

Then change the Items in your Gallery to colTest. Then, test your Remove formula again.
Remove(colTest,ThisItem)
If the item is deleted correctly, then we know there is some issue with your data source. OR, if we can't pull it into a collection, then we also know something else is going on.