Showing up to an onsite interview in a company shirt too brown-nose-y?

I have an onsite interview with a company in a few weeks. I have one of their company t-shirts, ya know, the free swag they give out at developer conferences, job fairs, tech talks, etc. It's actually

I have an onsite interview with a company in a few weeks. I have one of their company t-shirts, ya know, the free swag they give out at developer conferences, job fairs, tech talks, etc. It's actually a t-shirt for a specific product team in the company. Would I look like too much of a brown nose showing up to the onsite interview in that shirt? Maybe I look like I'm trying too hard to curry favor with them. Also, the recruiter said that they would hook me up with some free swag, definitely a t-shirt but could be other stuff in addition to that. Does that just make it weird if I'm already getting a free company shirt but I'm showing up in another one? Fwiw, I want to wear that shirt just because I think that product team is cool, not because I think they'll like me better or think I'm passionate or a team player or something like that.