SPOILER

http://fallout.wikia.com/wiki/Exterminate_the_deathclaws

So I've exterminated all the deathclaw & deathclaw mother and gone to see Gabriel of the Gun Runners. However, he just tells me "We need to be sure..." and "Let's give it a few days." I've tried waiting _weeks_ and nothing happens.

P.

EDIT: This is possibly a bug introduced by Fixt:

http://falloutmods.wikia.com/wiki/Fallout_Fixt_bug_reports

CONFIRMED - After installing 6.3 patch on top of 6.1, the Gun Runners won't acknowledge you stopped the deathclaws if you killed the mother before talking to them. [This is probably just a side-effect of increased number of local variables per script in the patch versions (overwriting memory they shouldn't be), but I'll test anyway, it's easy to test. --Sduibek]

Deathclaw eggs was destroyed too?

"To complete this quest, the Vault Dweller will have to kill the mother deathclaw and all her offspring, as well as destroy ALL FOUR DEATHCLAW EGGS in the basement where the Mother resides."

If not then after some time there will be new deathclaws...

Even if you do destroy all of the deathclaws including the mother deathclaw and the eggs...

...then report back to Gabriel and the gun runners...

...do you really believe the gun runners are going to just agree to turn over all of their ammo, weapons and armor over to you...? ...and let you leave unscathed???

:)

I'm just sayin'...