This thread is resolved. Here is a description of the problem and solution.
Problem: I am trying to click deliver/redeliver after a translation is finished inside the Advanced translation editor.
Solution: Using the clean Firefox install we managed to fully "Translate link targets" (in WPML/settings). In Chrome, whether in incognito or not, we could not fully run it. After the full run on the Firefox install, we now have it working on Chrome as well (as on any other browser for that matter).
This is the technical support forum for WPML - the multilingual WordPress plugin.