Step 1: Understand the meaning of "deny".
"Deny" is used when rejecting something factually, not when rejecting an offer.
Step 2: Evaluate the options.
- (1) said no: Less formal and incorrect for the sentence.
- (2) rejected: Possible, but "refused" fits better.
- (3) refused: Correct choice, as it is used to decline an offer.
- (4) no improvement: Incorrect because "denied" is not the proper verb here.