How to place Mirelurk Observer in Fallout 3

When you reach the place marked on your map open the egg clutch-container - it is the nest on the lowest level of the Anchorage Memorial. Then you should browse your inventory and manually place the Observer into the clutch - mission complete.

Maybe the description of "Fallout.wikia" can help you

The easiest and quickest nest to get to without confrontation of a single Mirelurk is the nest located behind the locked [Very Easy] door due southwest from the entrance to Tepid Sewers. After entering, make the first right turn. Directly ahead will be an egg pod. Place the observer and run out.

Stealth Boys are the best choice to reach the optional goal ;)