After some testing I found an easy way to backup tab sets links using a free web crawler named WebCopy. I am leaving here a mini tutorial of the steps I've followed:
Forms and Passwords
Log in using web browser
Uncheck "Download all resources"
Login with browser
Filter: exclude urls with "pinboard" (optional)
Export to csv
Delete urls with "pinboard" (if not done before)
Delete urls starting with "uri"