We'll have collaborative publishing in the near future. We don't quite have an eta for it, but it's in progress now. Check out our road map and give it an upvote! We'll let you know when we launch the new feature.
For now, the best thing you could do is used a shared email address for your team to log in. You can change your email address in your Account Settings. Also, could log out and head back to https://app.thegrid.io/ to get a new link which you could then forward to another person to have them be able to edit your sites.