Batch command to delete all subfolders with a specific name

Short answer:

FOR /d /r . %%d IN (backdrops) DO @IF EXIST "%%d" rd /s /q "%%d"

I got my answer from one of the countless answers to the same question on Stack Overflow:

Command line tool to delete folder with a specified name recursively in Windows?

This command is not tested, but I do trust this site enough to post this answer.

As suggested by Alex in a comment, this batch script should be foolproof:

D:
FOR /d /r . %%d IN (backdrops) DO @IF EXIST "%%d" rd /s /q "%%d"