You can reset 'Accounted' Trips to 'To be Accounted' (Recalculation) via report RPUREROL. In the SAP menu you find the report under Travel Management > Travel Expenses > Tools > Reset Status (transaction PRRL). Once the reimbursement is already paid or the trip is already posted you have to cancel the trip to be able to reset the status. Another alternative (e.g. to adjust an error handling) is to use report RPRTRVSW – the "crowbar".
 
With this report you can reset any trip status. The report documents this in the trip history.

Note: for security reason the report is not performable as it is. You are supposed to modify the report and mark the line ‚exit‘ with asterisks. If you don’t want to modify the report you can also
 
1. Create a variant variable in table TVARVC (e.g. Z_TRIPSTATUS) and fill it with an "X".
2. Create a selection variant for the report.
3. In this variant fill the hidden selection parameter EXTERN with your new selection variable.
4. Get the variant before executing the report and take other selections if you need before running the report.