“Plugin Update Available” shown when it isn’t

I hope I’m asking this in the right place, it’s more (I think) to do with managing my sites through WordPress.com than the Jetpack plugin itself.

I’m managing seven self-hosted sites, all connected to WordPress via a free Jetpack account. Yesterday, I used the “Manage Plugins” screen to apply some plugin updates, including updating the Jetpack plugin itself.

That turned out to be a mistake. The Jetpack plugin updates failed, leaving the sites in maintenance mode and some of the the plugin code missing. I had to go into each site, remove the .maintenance file, delete the rest of the Jetpack code and reinstall the plugin. No big deal, I won’t make that mistake again.

But now three of my sites show the orange icon claiming that they need a plugin update. If I select the site and go to its “Manage Plugins” page, it shows no plugins requiring an update (screenshot at https://snag.gy/kpavlj.jpg ). If I go to the site’s own admin, that also shows no updates pending. The *only* place where updates are showing as required are those dratted orange icons.

I’ve tried doing a manual sync from the Jetpack settings, but that doesn’t fix it. What can I do to sort this out?