What prevents Time Machine backup?
I would go with the general thrust of the suggestion of NoahL in comments (i.e. move the inProgress folder to the trash, disable SIP, empty the trash, reenable SIP, and then try backing up again).

However, if you do not know how to disable/enable SIP, you can follow these steps:


Start your MBP
Immediately hold down the commandR keys to boot into recovery
Click the Utilities menu and select Terminal
Type csrutil disable and press return
Close the Terminal app
Select Restart.... from the  menu


Once you've rebooted, empty the Trash (assuming you've already placed the inProgress folder in the Trash). Once emptied, shutdown your MBP and follow the above steps again, except that at Step 4 use csrutil enable instead of csrutil disable.