With foods from other countries, you should try to make an effort to pronounce them properly, so as not to offend those from that culture.
You would find it weird if someone kept ordering a burger, and was pronouncing it ridiculously incorrectly. Therefore, you should know how to pronounce gyro and shawarma properly.
Gyro is pronounced phonetically as ‘yeer row’. Whereas shawarma is said like ‘shuh war muh.’