You can’t delete individual messages on Tinder. However, you can remove entire conversations by unmatching someone.
When you umatch someone, you’ll disappear from their match list, they won’t be able to message you anymore, and they will also disappear from your match list.
To unmatch someone, go to your match’s profile > hit the menu icon (ellipses icon) in the top right-hand corner > Unmatch.
Please note that unmatching is a permanent action. If you unmatch someone, you will not be able to talk to that match again.