It is generally called the drawstrap or drawband.  Super easy to repair, just make sure that yours is intact, unrepaired, and retains the mounting hardware on either end.  Sometimes I see drawbands that have been stitched in the middle which can make them a bit too short to function properly.  I assume you are reusing the original?  When rewinding the mainspring on a standard desktop, usually the carriage is pulled with about 2 pounds of force.