I believe I had the same issue with some clips captured from a Hauppauge PVR. I have no idea why they chose mts as the "container" as it seems incompatible with many editing programs.
There are various conversion programs around that will produce REAPER friendly video -
I think I ended up using Handbrake.
https://handbrake.fr/
You need however to read this before downloading anything in this area:
http://www.makeuseof.com/tag/whats-p...ftware-remove/
Please post later when you get a solution cos I think I ended up with some quality loss (hard to say cos the originals were VHS!)