When there are modifications made to the Timesheet and when you transfer those Timesheet to a third party software using Repliconnect API, it is possible that it may not recognize the modifications made in the Timesheet.

One of the possible ways to achieve this would be to comparing the save date and time in Web TimeSheet and the third party application. If those doesn't match then the API can be used to program such that it modifies the time entries on the third party application.