Grills tend to affect the treble the most and works as an attenuation. If a speaker was intentionally voiced with the grills on then it will probably sound "better" with the grill on. Basically they probably add 1db or so to the treble so to counteract the attenuation caused by the grills.
The higher order affect of the grill is a little bit less apparent. A grill works like a filter, albeit a mechanical one, therefore it will filter out more and more toward the higher frequencies. That is the grill will attenuate the high frequencies but NOT by a fixed factor, but gradually toward the high frequencies. For example, at 10KHz, the attenuation is 1db, whereas at 15KHz it would be 1.5db, and at 20KHz by 2db. And like any filter, the grill will add phase shift to the higher frequencies and phase shift generally is not a good thing. A fixed 1db added on the tweeter probably will not undo the damage caused by the grill. It may help a little bit but won’t fix everything.
Regardless of the treble energy, removing the grill will most likely add some openess to the sound. By the way, "more trebles" does not mean "more openess".
The higher order affect of the grill is a little bit less apparent. A grill works like a filter, albeit a mechanical one, therefore it will filter out more and more toward the higher frequencies. That is the grill will attenuate the high frequencies but NOT by a fixed factor, but gradually toward the high frequencies. For example, at 10KHz, the attenuation is 1db, whereas at 15KHz it would be 1.5db, and at 20KHz by 2db. And like any filter, the grill will add phase shift to the higher frequencies and phase shift generally is not a good thing. A fixed 1db added on the tweeter probably will not undo the damage caused by the grill. It may help a little bit but won’t fix everything.
Regardless of the treble energy, removing the grill will most likely add some openess to the sound. By the way, "more trebles" does not mean "more openess".