Text reads;

"Whenever Eloe Kaffi becomes stunned, you may remove her from the game. If you do, characters you control named Hulk get +1 / +1. "

Does the +1 / +1 remain throughout the entire match? Or does it last just for the phase?

All Hulks that you control get that +1 +1. If you recruit a Hulk Later on after she has been removed he will also get the +1 +1.

From the MUN FAQ:

4. Warbound

Some Warbound characters have a power that says “When [this character] becomes stunned, you may remove it from the game. If you do, characters you control named Hulk [are enhanced in some way].”

Such an enhancement:

• Lasts for the rest of the game, even if [this character] card somehow leaves your RFG zone.
• Affects any characters you control named Hulk regardless of when they entered your control.

That is insane...

The Hulk legend is sick.