Normally, door undercuts over 1/2" will not maintain their 1-hour rating (used for toilets doors adjacent to corridors that are usually 1-hour rated).
Door grilles are seldom used nowadays for two reasons
1. If at hallways, then, they are a code violation nowadays, as door grilles are not fire rated, there may some rated doors with grilles, but it is your case?
2. transfer of room air to another, i.e use of a room as a return plenum is a code violation.
The question is: where and why a re you using door grilles to begin with?
you should use transfer ducts at ceiling with transfer grilles for toilet make-up air for example. if the wall is rated, you will need a fire damper at the TD. this is the general way things are done in the US, not door grilles.