Prospective Tenants Make Me Nervous - What Would You Do?

[Amethyst]

I am very nervous about a couple who want to rent our townhouse. My husband dealt with them, and he tends not to be as rigorous as I am about asking for information. He unwisely accepted a check for $150 for earnest money, which they now firmly believe means we have to rent to them as long as they provide a landlord reference, a myannualcreditreport.com printout, and some form of proof of income (which is what he told them). They haven’t yet provided their “myannualcreditreport.com” or proof of income, but with the small amount of information they have provided, I have been checking things out on line and things are not adding up.
The couple met my husband at the townhouse twice-once yesterday, once today. Each time, they were more than ½ hour late. They never gave their last name until the man wrote the check.
On-line court records on a man of the same name and age (it is not a common name) say he was foreclosed upon in May 2009.
Their check for the earnest money deposit, bears a different address than where they are currently living. But, on public records, the property on the check is listed as still belonging to the man.
The woman told me they are on a “month-to-month” lease (there is no such thing). She said they always pay their rent on time and the landlords will back them up on that. She stressed how clean and neat a housekeeper she is.
The place where they are renting is, in fact, registered to the people they call their landlords, but the property is listed as owner-occupied. This suggests to me that they are temporarily renting rooms in the landlords’ home, unless the landlords themselves are lying to the county to avoid paying the extra property tax on a rental property.
We are getting more and more uneasy with this couple. Would they have a case against us (discrimination) if we just gave them back their money?