In fact, the only live TMs in the USA for the single word "realtor" are for companies that use the single word "realtor" as a brand name for products unrelated to real estate brokerage.
Not sure of your source - or maybe you didn't look deep enough? - there are hundreds of TMs for 'realtor', best to check the
WIPO site for worldwide TMs (just type in 'realtor' in the Text field, hit enter). Many of those TMs are by the NAR. And they do include TMs for real estate services, like this U.S. trademark by the NAR for the single word 'Realtor':
BROKERAGE OF REAL ESTATE, INDUSTRIAL BROKERAGE, FARM BROKERAGE, MORTGAGE BROKERAGE, IN THE APPRAISAL OF REAL ESTATE, MANAGEMENT OF REAL ESTATE, IN THE BUILDING OF STRUCTURES ON REAL ESTATE, IN THE SUBDIVISION OF REAL ESTATE PROPERTIES, AND [ FOR CONSULTATIVE AND ADVISORY SERVICES ] IN COMMUNITY PLANNING FOR THE DEVELOPMENT OF RAW LAND AND SLUM CLEARANCE AREAS
The NAR also diligently pursues trademark infringers (and often wins). You can use
this section of the same WIPO site, type in 'realtor' (or any other keyword) to see a history of UDRP cases for that keyword, and see who won those lawsuits.
To OP: Also, in many cases a company does not need to have an actual registered trademark on their business name, in order to make a case for cybersquatting and to take a domain name from you. Use the trademark checker sites only as one level of reference; but also use the search engines, check out what companies are using an exact term as a business name and what their services are, etc. There is a lot more info to this than simply 'do they have a trademark on this term or not?'. Check out the legal threads here for more information.
Good luck