Let's say you've a trigger named trigger_obj2.
In the init.sqs:
"trigger_obj2" setMarkerType "empty";
When you want to activate the marker:
"trigger_obj2" setMarkerType "MarkerType";
Here the marker type can be any from the list, like arrow - flag - flag1 - dot. Depends on your preferance.
Don't think that you can actually hide stuff active in the briefing / notes. What you can do is to create a special section, with the following code in the briefing:
<hr>
<hr>
<h2><a name="obj2"></a>Objective 2<br></h2>
<h4>
Blablablabla text text text, the officer might be at mapgrid Ef67
</h4>
Most of the times I put this code after the objectives section in the briefing, so that's between the objectives part and the end of the html document.
Now, in the objectives part you do the following:
<p><a name = "OBJ_1"></a>Kill comrade Mantov</a></p>
<hr>
<p><a name = "OBJ_2"></a>Find the other officer. <a href="#obj2">More information</a></a></p>
<hr>
If you want to make things even more "perfect", I suggest that you give out a little hint to the player that his objectives have been updated. So in the trigger, or script whatever you use to detect if the objective has been completed:
hint "Objectives Updated";
Good luck.