When someone invites you out to dinner and offers to pay, the proper response would typically be to express gratitude and appreciation for their kind gesture. Here are some appropriate ways to respond:
"Thank you so much for the invitation! I really appreciate your generosity."
"That's very kind of you to offer. Thank you for inviting me; I'd love to join you."
"I'm honored you'd like to treat me to dinner. Thank you for thinking of me!"
"Oh, you don't have to do that, but I really appreciate the gesture. Thank you!"
"I'd be happy to join you for dinner. Thank you for being so thoughtful."
Remember to say it with sincerity and a smile to convey your genuine appreciation for their invitation and willingness to pay for the meal. If you feel comfortable doing so, you can also express your gratitude again at the end of the meal as a way to show your appreciation.