I have not worked with In-Memory OLTP in production, and I have certainly not tried it with log-shipping, so my answer is not the most helpful one.
The first thought that came to me is that you would need to perform recovery of the database to get rid of these files, but of course you don't want to do that with log-shipping. And my thought may be completely wrong; I have nothing to back it up.
Else: well, you can always stop the log-shipping and start again with a new fresh backup from production. Not pretty, but maybe acceptable if you only need to do it every third month or so.
I will need to admit that I don't understand the message Cleanup of stale DB entries skipped because master db is not memory optimized. Master is typically not memory-optimized.