In this type of situation, I would usually run through the following checklist:
1. Is it an intent-to-use application or a use-based application (indicated by "1(a)" or "1(b)" in the application?
2. If it is a 1(a) application, what is their alleged date of first use?
3. When was the applicant formed? This is usually determined by looking at the applicant and their charter jurisdiction (stated in the application itself), going to the relevant Secretary of State (for US), looking up the applicant, and checking their date of formation.
4. What other information can you determine on use of the mark by the applicant (or an individual predecessor) by searching Google, their website, etc..?
5. What kind of term are we talking about here? Generic, descriptive, suggestive, arbitrary, or fanciful?
6. What is your domain name doing? Is it doing anything relevant to the goods/services of the applicant (or, in the case of generic or descriptive terms, is it doing something relevant to the generic/descriptive meaning)?
Those are the kinds of things you would want to figure out before deciding what, if any, course of action is preferable.