it says I need the article 'a' here. but there is no 'a' here. well there is a 'the' but then the message is not correct
Ukrainian sentence can mean eithe 'They are looking for a new overcoat' or 'They are looking for the new overcoat'. The exact meaning depends on the context.
Yes I know that "the" could work as well, but the question here is - there is no "a" in the suggested words, but in message it says that I need an "a".
This is a bug in the course. The recommended ways to report such bugs is the 'Report' button. Since you've written in comments, I've assumed you weren't sure if it was a bug or not, and that's why I've written my answer. :)