To minimize the changes inside the VM disks, I've be moving the paging file to a separate virtual disk. We can then exclude this disk from the backup process.
One one VM (and only one) we got the following error:
Windows created a temporary paging file on your computer because of a problem that occurred with your paging file configuration when you started your computer. The total paging file size for all disk drives may be somewhat larger than the size you specified.It turns out that on this particular virtual machine, we needed a total of four virtual disks. This combined with the virtual DVD drive meant that we needed to use SCSI disks in the VM. In a Hyper-V VM, you cannot place the paging file on a virtual hard drive on the virtual SCSI bus. The virtual SCSI bus is not available early enough in the boot process.
So, in this case, the easy fix was to move the paging drive to be an IDE disk and all was good.
Microsoft has a knowledge base article to this effect: