Does your Master’s matter in the US if you have a good undergrad degree?

Currently in an IR role at a MM PE in Asia, but looking to leave my job and pursue a Master's in Finance abroad in order to transition into the sell-side (IB) with a target for front-office PE (Deals Team) over the longer term.

This was my first job out of college and only been in it for about a year. I took it because of Covid and my visa situation. I did my undergrad from a U.K. target (LSE/Oxbridge etc), but only had 4 months before my visa expired to find a job. I liked the U.K. but I think it's a very small market to be in and so want to transition to a larger market like the US.The Master's programs I'm looking at in the US though are mostly semi-target / mid-tier. It wouldn't be impossible to hustle my way into an IB role from them but also not as easy as if I was at a target. But to what extent does your Master's degree even play a role in US IB recruiting, especially if you already have an undergrad from a target uni (not just in the U.K. but globally)?