If the Vault Dweller chooses to kill Razor and/or make the Blades hostile, the Gun Runners will become hostile, preventing access to this quest. So it's best to wait until completion of Exterminate the deathclaws.
The basement the Deathclaw Mother resides in has no light sources, and thus the chances of hitting with guns will be reduced without Night Vision or the use of flares.
Note that even if the eggs and the Mother are killed, there might be a deathclaw at the top of the sector, easily missed.
After completing the quest, move out of the sector and run back to the Gun Runner's territory in less than 2 days. Then the Vault Dweller may be able to gain 1000 XP each time they do so. [verified]
While the chances of hitting the mother deathclaw in the basement without using flares or having Night Vision are reduced due to the lack of light sources, the chance of hitting the Deathclaw eggs is not reduced, despite them being in the same dark corner the mother deathclaw is found in. [verified]