Usually job applications are filtered by recruiters first before they are seen by the people you would actually work with. Recruiters are likely to have less subject-specific knowledge and may pay more attention to things like well-known universities. So it might help you in the initial filtering.
The rest is almost entirely dependent on different factors.
If you were to get an interview following initial filtering it's likely to not matter much at all - unless one of your interviewers happens to have gone to your uni or know someone well who has, they're pretty unlikely to bring up your uni by name at all. They might ask you what was covered on your course /what modules you studied, so on - but it's more to get a grasp on your skills than to assess how "good" your uni was.
Then it's likely to come down to how well you interview - if you have decent social skills/seem like you'd be easy to work with, if you approach technical questions in the right sort of way, if you seem comfortable and confident in presenting yourself and your work without being cocky. If they believe you have enough technical skill to complete the work they would be asking of you, if you would be receptive to learn.
Don't take my word as gospel or anything, but I think if you can get the interview, your uni is pretty unimportant.