The easiest way would be through bulk editing. Just select all the tickets that have a value in the labels field, and when you bulk edit them click the checkbox next to the labels field. As long as you don't type anything in the labels field on the bulk edit screen it will remove any value in the field for those tickets (essentially overwriting what is there with nothing).
If you have tens of thousands of tickets, though, there might be a more efficient way.
As far as I know, the choices displayed are suggestions based off of the values of data currently entered in the Labels field for all issues. If you remove all the current data from that field (as per my previous instructions), then you should no longer have any suggestions available in the dropdown.
I tested this in my dev instance of JIRA by removing all label data, adding "test" to the label field in an issue, then removing it. When I went to edit the labels field for the issue again, there were no longer any suggestions present, including "test".
I would suggest that you create the new protocol for using the Labels field and communicate it to affected users first, however - otherwise you'll probably have to re-do the process.
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