In order for NCR Command to better allocate supplies to their forces (including those at Forlorn Hope) they need to know what troops are dead. The easiest way to prove this for field troops is to bring back the NCR dogtag from each body. Therefore, Quartermaster Mayes is offering a reward for bringing those dogtags to him. After discussing the supply problems Camp Forlorn Hope is having with Quartermaster Mayes, he asks you to collect dog tags from fallen NCR soldiers.
After you turned in fifteen dogtags you'll get a special reward from Mayes, consisting of 100 bottle caps and 6 beers, but you have the option to refuse the reward and will earn good karma.
The payout per NCR dogtag is small. Aurelius of Phoenix will offer more, 10 bottle caps per dogtag or after a Barter check of 35, Decanus Severus will offer ammunition and other supplies. Neither will accept irradiated NCR dogtags. You get Legion fame for turning them in to Aurelius of Phoenix or Decanus Severus.
There is bonus applied to the third part of Restoring Hope. Every five dogtags turned in adds a morale bonus of one for a maximum of three. This bonus is applied to the Nelson attacking forces.