Honestly, I never mention it in real life unless directly asked because people (especially in tech, I've noticed) seem to be very sensitive around "name-brand" schools, ie. with comments like this.
But I think it has direct relevance to the GP comment.
I've read this here before but I honestly think there should be more regulations about who can be hired. The name of the school should not matter in the slightest if one has studied the same thing.
Making it impossible for the employer to know that detail would also incentivize all the schools to provide a good education. Also many top universities are mostly about making connections. While their curriculum is usually very hard, this is also reflected in the grades.. people may still pass but their average drops.
In the US it's even worse, because tuition has to be paid. This already filters out many people from going to a "more elite" school.