Din of the Damned and Eyes of the Wild

Does Din on the Damned increase the cost of an Eyes of the Wild when it is played?

What I think it is not clear here is the "grants intercept" sentence. Eyes of the Wild does not grant intercept inmediatlly, but it could grant it by its own effect.

Din of the Damned
Type: Action Modifier
Clan: Harbinger of Skulls
Card Text:
Only usable on an undirected action as the action is announced.
Equipment and conviction cards cannot grant intercept this action (any intercept they grant is lost). Reaction cards (and powers) that grant intercept for this action cost an additional blood or life.

Eyes of the Wild
Type: Reaction
Clan: Gangrel
Card Text:
Only usable by a locked Gangrel.
This Gangrel unlocks and attempts to block. During this action, this Gangrel can burn 1 blood to get +1 intercept. Lock this Gangrel after action resolution if they did not block this action.