Found this on the Side of the Street While Walking Home.
It seems to be some type of hat? It's Port Authority branded. However I cannot find any images of this hat online that has the DQ symbol like this one. I have also been unable to find any mention of it as being part of the uniform. It seems like it would be part of a cold weather uniform but it is May and I'm also in Texas.
None of this is a big deal, I was just curious and bored on a Sunday and thought someone on here may no a bit about it.
Side Note: I just learned recently that other states do not have the T-brand tacos on their menus which is a travesty. They taste so much better than Taco Bells, they are larger, and their ingredients are fresher/higher quality. Not to mention they do $1 tacos for Taco Tuesday. If you ever get the chance definitely get the tacos.