A one-star reply is not a conversation with the person who wrote it. They have already decided. It is a note to the next person, who is reading the review and the reply together and deciding whether the bad day was a one-off or the house style.
That changes what the reply is for.
What works
Answer in two to four sentences. A long reply reads as a defence. A short one reads as someone who has already dealt with it.
Name the specific thing. "A fifty-minute wait with no explanation" tells the next reader you read the review. "We are sorry you had this experience" tells them you did not.
Say where it went. "The manager on duty has the detail" is a fact a reader can weigh. "We take all feedback seriously" is not.
Take the specifics off the record. Not with a phone number the reviewer never gave you — invite them to reply, or to use the contact route already on your listing.
Use the first name or no name. Never the full name. It reads as a file being opened.
Post it the same week. A reply four months later is dated in public, next to the review, forever.
What makes it worse
Arguing the facts. Even when you are right. The next reader cannot adjudicate it and will not try; what they see is a business that argues.
Denying the visit. If it is genuinely not your customer, report it — do not litigate it under the review.
Offering money in public. A refund in a reply teaches every future reader what a one-star review is worth.
The same opener on every reply. Five "Thank you for taking the time to write this" in a row under five different ratings is the tell that nobody read any of them.
Why StarReply will not post this one for you
StarReply drafts the reply to a one-star review — so the hard one is already written when you open the queue — and then holds it. Not as a default; as the first branch in the routing code, in every autonomy mode, with the database refusing to clear the flag.
The reading, the sorting and the drafting are work a machine should have finished overnight. The decision, on the review that could actually cost you a customer, is the part that should still be yours.