Is "received with thanks" stilted English?

Dictionary.com defines stilted as "stiffly dignified or formal, as speech or literary style; pompous." Named synonyms include terms like artificial, affected and forced, which imply something unnatural or insincere. Official and business writing tends to be formalized in an attempt to make it sound sincere, even though the result may be just the opposite.

In this case I'd say the phrase received with thanks in written form deserves the benefit of the doubt and isn't stilted, especially if it is routinely used in the course of business.

On the other hand, if someone said to me "I received with thanks the sum of 10 dollars from that fellow over there," that would strike me as very stilted (or I would think I was in the middle of a Dickens story).

In any event the expression is definitely formal enough on its own.

It is not old-fashioned or stilted. Writing "received with gratitude" would be more old fashioned and stilted.

More formal... leave off the thanks! See an example here: http://www.agriscience.msu.edu/specialprojects/Chapter%20Officer%20Development-Michelle%20Guthrie/TREASURER/9%20WRITING%20RECEIPTS.pdf