This thread is retarded, some girl at the front counter said hi to you, you didn't say hi back, so she got mad cause you were being rude.
It is in fact her job to meet & greet, as well as say goodbye to everybody walking in and out of the gym. So when she says those things, most people expect others to have the common courtesy to return the hello or goodbye, regardless of how ingenuine it may be. You did not display that courtesy so she called you out on it.
You're overreacting, I doubt she's interested in you. She's looked at you while you were working out because there is nothing to do in the gym. You're there alone most of the time by yourself listening to music, there isn't really much to do besides look at other people to see what workouts they're doing, what techniques they use, etc. For the people that work there it must be even more boring cause they're not even exercising, they just stand around and do nothing.
Move on and get over it. It's not going to be "awkward" when the lady at the front desk says hello and goodbye to you like she does to every single other person who walks in and out of the gym.
What are you in high school?