"Declined with thanks" is a polite and respectful way to decline an invitation or offer. However, there are many other ways to express this sentiment. Some common synonyms include "regretfully declined," "respectfully declined," "politely declined," "graciously declined," or even "sincerely declined." Each of these phrases conveys a similar message of appreciation for the offer or invitation while politely declining. It's important to remember that declining an invitation or offer should always be done with gratitude and kindness, whether it's done in person, over the phone, or in writing. Using an appropriate synonym can help convey that message in the most respectful way possible.