Is the blocked list just regular contacts that are blocked?
If they are contacts synced to your Google account, they should restore automatically when you sign back into your device after a factory reset.
To be double safe you might want to open your contacts app and go into the 3 dot menu and export your contacts. Then take that export file and copy it to your PC.
This way, if for some reason your contacts do not restore properly, you can copy that file back to your device and import the contacts from your export.