With remarks, red doesn’t indicate “not yet achieved” and gray “achieved”. Red means that the remark has been assigned to you, or that it is still unassigned. Gray means that it has been assigned to someone else. So if you post a remark and assign it to the translator, he will see it as red and you will see it as gray. If you leave it unassigned, or assign it to the whole team, you will both see it as red.
Once the issue has been dealt with, you or the translator will click “resolve”, and the flag will not change color, it will disappear. You can still see all the resolved remarks if you open the project notes and filter them by “resolved”, but resolved notes will not show a flag or any other kind of tag in the text window.