Illegal Equipment on Pitcher?

 
In the top of the fifth inning, a new pitcher enters for the home team. As he takes his 8 warm-up pitches, the defensive coach notices that the new pitcher has a batting glove under his baseball glove and asks that it be removed. Must he remove the batting glove?
 
What if the defensive coach notices that the new pitcher is wearing sun glasses. Must he remove them?
 
Call
In NF (and only in NF), the pitcher is permitted to wear a batting glove under his baseball glove.
 
If the umpire judges that the batting glove is distracting, then it should be removed. Several that answered the quiz added that they would have the batting glove removed if it contained white or gray. My understanding is that the white/gray prohibition applies only to the pitcher's baseball glove and the pitcher's sleeves.
 
A pitcher is permitted to wear sunglasses (despite many coaches claims that they must be removed).