Thanks for the reply.
I used the Media Cleaner plugin to remove media entries where the files are missing.
But now reSmush.it gets stuck in the “Examining existing attachments. This may take a few moments…” phase.
I checked the WordPress error log and there are no more entries related to reSmush.it.
There are no errors in the browser console.
The reSmush.it log shows only this:
Bulk optimization launched for file : [site home]/public_html/wp-content/uploads/2016/04/[file.png]
Revert original image for :[site home]/public_html/wp-content/uploads/2016/04/[file.png]
And then the log stops. I guess there must be a problem with that particular file, but there’s nothing else in the logs…