Sure thing! Nope, they won't have. That class of antibiotics isn't associated with any impact on oral contraceptives, period, but it also turns out that most of the time, antibiotics and oral contraceptives aren't something to worry about no matter how you slice it or what kind you're taking.
There are a couple exceptions to this, and some subtle nuances, though. That's explained well in more detail here: https://www.scarleteen.com/article/bodi ... th_control
Something to know, though, is that using condoms can both help prevent UTIs AND is a good backup, just as something to consider, especially if you're getting UTIs often. Another thing to know, since you're using the pill, is that part of the way the pill works makes the vagina drier by design, so if you're not using extra lubricant with sex (both with and without condoms), that can also be something that makes UTIs more likely, as drier genital tissue is less resilient and the connection of the vulva and vagina to the bladder is such that dryness can increase your likelihood of urinary tract and bladder infections.