This thread is resolved. Here is a description of the problem and solution.
Problem: I want to translate a word on the checkout page of WooCommerce, because it seems it is not yet translated. When going to the string-translator, I find the word. But it shows up with the wrong language. Then I change the language and translate the word. When reloading the page, still the word shows up without translation. Solution: Just uncheck the Assume that the original language of all strings is English option from the Dashboard → WPML → Theme and plugins localization area and everything will go back to normal.
This is the technical support forum for WPML - the multilingual WordPress plugin.