tt-615680 - Wednesday, February 7, 2018 6:20 AM
The error message is typically caused by permissions. I have no idea what \\Directory is pointing to or what directory was in the error message, That series of errors is exactly what you get with the permissions issue. You'll need to figure it out by going through the sp_MSdistribution_cleanup stored procedure the job executes.
Here is a blog post about the error - it basically says the same thing I posted in my first reply:
Distribution Agent fails with “Could not remove directory†error
Sue