When viewing the contents of your G: Drive you might see a few or a lot of files that start with a ~$. Something like this.
These are temporary files that Microsoft Office creates to store change information on a document as you work on it. This is normally hidden from view, but the migration captured all of the files present and migrated them, so you now are seeing these files. They are completely safe and were present, but hidden from view on your original H: drive. It is safe to ignore these files or delete them if you so wish.