How do you respond when someone says "Thank you for your service"?

I always thank them, offer my hand for a shake... Sometimes I reply with a "You are/were worth it". Regardless, I share my appreciation for their comments.

I’ve heard the response “You were worth it” also

I used to say thanks with a smile, but now, since my larygectomy last September, I give a thumbs up and smile :)

Depends on who says it. Most WW II combat vets saw more combat that I did, so I get humble.
Older civilian, I say "you are welcome"
Good looking single lady gets an opportunity to thank me.
For an 18 - 35 y/o male, I offer to take them to the Recruiter. When they say they are too good or important to serve, I bite my lip, chuckle, and walk away.

I respond: As a Veteran, I thank you for being someone worth serving for (if they seem worthy of the response). I may then add: and I would gladly serve again, but not under the command of the current President.

Thank you. However, I feel for the most part their statement was hollow as I started during Vietnam and finished with Desert Storm. With hostility was my greetings of the time. Today if I say I served during Vietnam, I am still treated with hostility or disdain in their voice. I had a Statute in my front yard which was upended and thrown to the ground about a year or so. It was a Soldier carrying a wounded soldier. It had a Dog tag around its neck. That was my Brother's Tag. My Brother was Infantry: C company 2nd 502 101st Airmobile Vietnam. I was attached as a Reservist to HHC 6th 502 101st Inf. Reg-Berlin year 1986. However I also served during Vietnam on Active Duty not in country. My last Active Duty MOS during Desert Shield and Desert Storm was Combat Medical Specialist 91A E5 and AD for Desert Storm was 91B E6. I was proud of my brother's service and as he stood in for me during Vietnam, I took a stand for him through his remaining life as his readjustment to America never occurred until a few days before he died in 2015. That is why the statute was placed in honor my Brother. I found his Dog Tag bent over and stomped on where the statue was originally placed in my front yard. And that is why it is hard for me to accept someone saying "Thank you for your service." With respect I will say thanks in return but I feel hollow inside when I say it.

While it can, sometimes, make me feel a bit uncomfortable, I always try to be polite. They are trying to be nice, and it's a much better reception than many veterans received back in the 1960's.

Thank you, it was an honor to have served.

I had a friend say "Thank you for your support." and that stuck with me. That's what I've been saying from then on.

“Thank you. It was my privilege and honor to serve this great Nation and its citizens. Your thanks prove that we continue to be a great Nation today…it was my honor to serve and my honor to have your recognition for that service.”