IANAL, but they almost certainly don't need permission. Typically you just need a message that says X is a registered trademark of Y. GitUp is unaffiliated with Y.
Also, it's entertaining to me that in one comment you say that closed-source proprietary software is bad, and in another comment you're concerned about whether they follow trademark law. I understand that it's not a direct comparison and open source software is still subject to IP law; it's just that the juxtaposition of your comments is a bit silly.
Talking about "IP" law as one thing is useless. There's certainly no real-world validity to the idea that ideas are property, but even if we accept the legal concept of it…
Copyright is a restriction that mostly censors the sharing and building of ideas freely. It should be abolished. But it's currently used to deal with plagiarism and to support copyleft licenses. We should have stronger legal protects for attribution, against false endorsement claims, and support technology freedom with mandates for source release for published works and prohibition of DRM.
Patents are just bullshit. We should abolish patent law and just have better social systems for grants and funding for research (although it might already be true that almost all useful patentable inventions are built on socially-funded research already).
Trademark is a consumer protection. It is absolutely essential. It protects people in the market to know that they are dealing with the same legitimate entity when they see the trademark in use. There are cases of abuse or of it being overly strong, but trademark is totally important and basically positive.
IP law is pretty important to open-source keeping rights to names too, and git is open source (GPL v2 IIRC). Don't see the contradiction, as parts of IP law are needed to make sure contributions remain open.
Also, it's entertaining to me that in one comment you say that closed-source proprietary software is bad, and in another comment you're concerned about whether they follow trademark law. I understand that it's not a direct comparison and open source software is still subject to IP law; it's just that the juxtaposition of your comments is a bit silly.