If your tree s grafted and they are from below the graft line, YES

How do you know they are 'orange' branches? Are they bearing oranges?

pix are worth another million woreds

I was told by a Garden center they were. No fruit. How do you tell where the graft line is??

Ken,I will take a picture tomorrow.

Graft line is usually down low, near the soil. They probably told you it was sour orange which is a common rootstock.

Top is lemon. Bottom is orange.

Sounds like they should be cut off. I will do that. Thank you everyone!!!

Yes, cut all the branches off that have 'trifoliate' leaves. Look up trifoliate if you don't know how to identify them. This is your rootstock that is trying to sprout and grow. Cut them off as close to the main trunk as you can. You don't want them to resprout and you don't want them to get the upper hand or your Meyer will eventually give up.

FYI, Poncirus trifoliata is not really an 'orange'. It is a citrus relative commonly used as rootstock, but the fruit are far from palatable.

Dave gives good advice...Nice