They entered, left the country and now they are coming back. Right?? How did they first entered Qatar: Visit Visa? Family Visa? Tourist Visa??

As per Qatar immigration rules US citizens are granted Visa on Arrival. So they should not have any problem.

Anyway some info for you:

http://portal.www.gov.qa/wps/portal?New_WCM_Context=/wps/wcm/connect/cnt...

Regards!!