There is a gray line between "refurbisher" and "remanufacturer". My understanding is that FDA in practice considers the former term to apply to a company that obtains used equipment, cleans it up and re-markets it to a new user; with the latter applying to a company that performs repairs to equipment that is significantly out of original performance or safety specs, so as to bring it into those original specs, or new specs that make it clinically safe and effective in some different manner.
If your role will fit the "remanufacturer" definition, then very generally in the absence of further information about your company, your responsibilities will be:
1. Register.
2. List all the devices you will work on.
3. Set up and maintain a QMS, including all of the actions needed for your organization under that QMS to be conforming.
4. If the devices you work on are radiation emitting, file the appropriate reports.
To make things just a bit murkier, FDA has another type of activity - "reconditioning" - which in my understanding corresponds with "repair" or "fixing" in everyday language. The way I understand the (long standing) status-quo, this type of activity is generally not overseen by FDA.