If OP has first use in commerce that predates theirs they could start, or threaten to start, the paperwork to have the trademark tossed. If they see you are asking questions that aren't a response to bullying, but that would precede a legal an attack their trademark directly, they might find themselves on a different footing.
Regardless, the possibility, I would think puts you in a better negotiating position if you're looking for an offer, or just want to make them go away.
Seeing a lawyer is likely the way to go. Also, I notice you use the term "solicitor" which makes me think any US law-based answers are less likely to be grounded in reality for you, so add more than your usual pinch of salt to anything you see here, including what I wrote!
"This past June, the U.S. Supreme Court ruled that plaintiffs cannot sue companies in a state where they may do business, but do not have significant connections to that state."
Bristol-Myers Squibb Co. v. Superior Court of California (BMS)
https://www.andruswagstaff.com/blog/supreme-court-rules-plai...
obtw there's serious risk of trying to defend a suit yourself. Maybe the judge would take pity on you and grant a continuance for you to find counsel.
"Don't solicit for your sister, that's not nice. Unless you get a good percentage of her price." -Tom Lehrer, Be Prepared
If not - they'll auto-win and Verisign will happily transfer the domain to crooks.
I'd evaluate what your endgame is. If your endgame is to keep the domain then I'd get a lawyer in order to make it clear that you will respond to legal challenges (and, yes, the bill is going to run up). If you were willing to sell, for a price, then you should try to figure out how much a legal challenge would cost them and set a price a bit higher than that.
Is it fair? Absolutely not, but the US legal system is set up so that those with the deepest pockets often win. It isn't a fair fight for normal citizens, and even having the law on your side is often not enough because it is a financial battle more than a legal one.
Either way may be wise to lawyer up today, either for a better selling price, cause them to back off entirely, or move it into the "bury you with costs" phase of bullying.