[sudo-users] What are sudo timestamps used for?

[Todd C. Miller]

Sudo uses the time stamp files to track when you last ran sudo in
order to determine whether it should prompt for a password.  By
default, if you've run sudo in the past 5 minutes you don't need
to enter the password again.

Older versions of sudo use one file per login terminal.  Sudo 1.8.15
and higher uses a single file per user that contains multiple
records.

You can safely remove the time stamp files, they will be recreated
as needed.

 - todd