How to remove a stripped bottle cage mount?
If the threads in the rivnut are okay, you may be able to re-compress it using a matching threadded bolt and some matching nuts.   Or you can buy/borrow the proper compression tool.
A temporary repair might work to force some JBWeld down the sides, and have it essentially &quot;glue&quot; the rivnut in place.  This may last for ages or fail on the first ride.
If your rivnut is stripped, you'll need to remove it and replace with a fresh one. The problem here is that there may be enough damage to the frame that getting the old one out is hard, and a lack of &quot;meat&quot; for the new one to attach to.
The solution then is to silver-solder in a new threadded insert (not a rivnut)  This will doubtless marr the paintwork to some extent.
As for costs, we can't tell you.  Instead, ring up your LBS and ask directly about a bottle cage boss repair.
Lastly - do use antiseize compound or grease on your bolt threads in the future.  This is where it shines.