It might help a lot if you could tell us what an EGH score was. That way, we could look it up, and figure out what the underlined part means. As it is, Google is being exceedingly rude by refusing to look it up, simply changing "EGH score" to "high score". Google Search is very useful, but it's becoming just a bit too arrogant lately, and forgetting its place.
PS: This might help: "One measure of efficiency for residential buildings is the EnerGuide for Homes (EGH) rating." I find the original sentence mystifying too.
Student or Learner