Tarring files in Linux 6.5

So we have 544 Linux machines
They all send their audit.log to the syslog server

Some of the logs are getting quite big and need to be tarred/compressed and stored on the backup sever to be backed up.

So I wrote a script that tells me what folders are over 1 gig
du -h --max-depth=1 /mnt/rsyslog/ | grep '[0-9]G\>' | sort -hr >/mnt/rsyslog/audit/Over1G.txt

That gives me a listing of folders that are over 1G and outputs to the text file

Currently I am having to go to each folder and tar the file to the backup server, remove the file, then remove the directory.
repeat steps for next machine

Is there a way to write a script that will do what I do via the script?

Attached is what I do.

Thanks
John
tar_experts.txt