Can creatures with Undying or Persist escape from Grave Betrayal?

Question

Can creatures with Undying or Persist escape from Grave Betrayal?

702.78a Persist is a triggered ability. "Persist" means "When this permanent is put into a graveyard from the battlefield, if it had no -1/-1 counters on it, return it to the battlefield under its owner's control with a -1/-1 counter on it."

702.92a Undying is a triggered ability. "Undying" means "When this permanent is put into a graveyard from the battlefield, if it had no +1/+1 counters on it, return it to the battlefield under its owner's control with a +1/+1 counter on it."

Answer 1

Yes. According to Gatherer, Grave Betrayal creates a delayed trigger that looks for the original corpse:

Each creature you don’t control that dies causes a delayed triggered ability to trigger at the beginning of the next end step. If there are multiple such abilities, you can put them on the stack in any order. The creatures will return to the battlefield one at a time as each ability resolves. The last ability you put on the stack will be the first one to resolve.

If the creature card leaves the graveyard before the delayed triggered ability resolves, it won’t return to the battlefield. This is also true if the card leaves the graveyard and returns to the graveyard before that ability resolves.

Answer 2

Yes (assuming the creature didn't have the relevant counter on it when it died).

When a card changes zone, it becomes a new object with no relation to the object it was in the earlier zone. (There are exceptions that allow Persist, Undying and Grave Betrayal to find the card in the graveyard, but the exceptions don't allow them to find the cards if they move from there to anywhere else.)

400.7. An object that moves from one zone to another becomes a new object with no memory of, or relation to, its previous existence. There are seven exceptions to this rule: [...]

As such, once persist/undying moves the card from the graveyard to the battlefield, the object Grave Betrayal's delayed triggered ability effects ceases to exist. When the ability triggers at the beginning of the next end step, it will have no effect.

This is the case regardless of whether Persist/Undying or Grave Betrayal resolves first (which depends on whose turn it is), since Grave Betrayal's ability merely creates a delayed triggered ability that will have effect later.

If the card were to find itself back in the graveyard before the beginning of the end step, it would be a different object and wouldn't be affected by the delayed triggered ability created the first time it died. (Of course, if Grave Betrayal is still on the battlefield, it'll create a new delayed triggered ability the second time the creature dies.)