@HRproSarah_9 — Trademarks are territorial. A UK registration gives them zero rights in the US. If they don't have a US registration or significant US common law rights (actual use in US commerce), their C&D has no teeth domestically.
That said, if you're planning to expand to the UK or EU, or if you sell to UK customers online, it gets more complicated. Also check if they filed a Madrid Protocol application that designates the US — that would show up in USPTO records.
Many UK/EU companies send these letters preemptively hoping you'll just comply. A polite response pointing out jurisdiction usually ends it.