They were ____ embarrassed by the reports that came out after they thought it had been forgotten.
Ok, this is a total per peeve of mine! Few people seem to understand the words" further" and "farther". I think everyone understands that both words are used when speaking relatively. But few seem to get the distinction between the two. Unless you are actually referring to distances, the word "further" should be used. "Further" is really a special-use version of "farther" for distances. Where people go wrong is that they think "farther" is appropriate any time they are talking about geography at all. "He walked a little bit FARTHER" is WRONG! I corrected an AP News writer recently because she kept writing the phrase "farther inland". She wasn't referring to absolute distances but just relative position. So, even though geography was involved, the correct phrase is "further inland".
here is the rule:
further(but not farther) can also mean: more or addicional.
so, here the sentence pointed out how more embarrased they were