Wiktionary
regrets only
n. (non-gloss definition: Written on an invitation to request that the invited person reply ''only'' if they will not attend.)
Wikipedia
Regrets Only
"Regrets Only" is the 16th episode of the second season of the American sitcom Modern Family, and the series' 40th episode overall. It aired on February 23, 2011 on ABC. The episode was written by Abraham Higginbotham and directed by Dean Parisot. Its original American broadcast was viewed by an estimated 10.35 million households and received a 4.1 rating.
Usage examples of "regrets only".
She regrets only that she did not jump at Berel's offer to deliver Louis.