You can use sshfs or samba to mount a network share to your computer

after mount you can make a copy of the hole drive with your data with the dd command

list drives with lsblk than make a copy with

Example: Your drive is /dev/sdx

Your mounted folder is /mount/backup/

dd if=/dev/sdX of=/mount/backup/yourdrive.image bs=1M status=progress

You can also make a backup of the needed folders if you don't want to make a whole backup of the drive with rsync or cp

At the end you need space, you can compress but i don't know if you win much space on the remote machine or buy a new usb stick or a harddrive and do the backup on the new drive

You can use sshfs or samba to mount a network share to your computer

after mount you can make a copy of the hole drive with your data with the dd command

list drives with lsblk than make a copy with

Example: Your drive is /dev/sdx

Your mounted folder is /mount/backup/

dd if=/dev/sdX of=/mount/backup/yourdrive.image bs=1M status=progress

You can also make a backup of the needed folders if you don't want to make a whole backup of the drive with rsync or cp

At the end you need space, you can compress the whole thing but i don't know if you will gain that much space and if the space on the remote machine is enough or buy a new usb stick or a harddrive and do the backup on the new drive