Market Drayton Town Council faced criticism in October when it announced it would enforce a pre-existing rule banning "articles" on grassed areas away from plinths.
The decision was made after complaints that some people with mobility issues couldn't get around the cemetery to their own families' graves because of the obstructions.
The deadline was today, December 2, but some townspeople were adamant they would not move items.
The town council has made headway with most people now though, said town clerk Julie Jones.
Speaking at a meeting of the town council's services & facilities committee on Thursday, she said: "Most people I've spoken to, once I've explained, they were quite reasonable.
"Most of the articles have been removed. We may have to write to one or two individuals who basically won't do it.
"I have tried to talk to the people and they have been quite reasonable. I think we're having quite a lot of success."
Councillor Tim Beckett agreed and said that some people could not maintain their families' graves because of obstructions.