We don’t have any specific petitioning system, the most we have is a way to vote for specific issues on bugzilla. This is related to core functionality of Thunderbird though, not add-ons.
While we would love to pick up the tab (no pun intended) for each add-on out there to make sure they continue to be a great addition to Thunderbird, this is something we need help from add-on authors for. I think the best approach would be to get in touch with the add-on author and ask them to update the add-on.