In the 1980s I read a short story in an anthology that also contained "The Ruum" by Arthur Porges and "Tickets Please" by D H Lawrence. The short story featured a group of possibly British people staying at a hotel. An old man claimed he could make anyone disappear totally, so that no one would even remember they had ever existed (no photos, physical evidence, memories of the person, etc.). No one believes him so he does it, and the story ends with a young newly wed man kicking over a stool that his bride (Jessamy?) had been sitting on, but she is no longer there, so she was the one who was totally eliminated. But no one believes the old man actually did what he claimed because no one could remember the young woman having been there, not even her new husband. I always found it a bit chilling and creepy, but can't remember what the story was called.
It was a little tricky to pinpoint, but the effect of the powers described is on TV Tropes called Ret Gone. At first, after reading through their list of literature containing this trope, I thought it wasn't there.
But then I noticed the last entry, which lacked the usual summary and decided to look it up elsewhere. And there it was.
I believe what you are looking for is Exit by Harry Farjeon.
Mr Geeles: ... He is old, on his own, has not joined into anything, has special powers...
Jessamy: young woman who should not have been decreated as she had done no wrong. She was in love, frightened of whole process. Mr Geeles selected her as he could not stand to see the young couple happy. Nobody notices he has been decreated even her husband.
I think it was "Exit" in a book of short stories. It ends with the vacant chair being kicked over and the participants thinking it hadn't worked.