Ms Ashfield said she was concerned when the cheque arrived.
A council department has been criticised for sending a cheque for over £30,000 to the wrong house.
The error came to light when the recipient at Aber-erch near Pwllheli, contacted her local councillor.
The cheque, which was meant for a householder 10 miles away near a new bypass at Clynnog Fawr, has been returned to Gwynedd County Council.
A council spokesman apologised for the error and said procedures were being reviewed to prevent it happening again.
The cheque - for £31,500 - is believed to have been intended to pay for a compulsory purchase of land for the construction of the A499 Clynnog Fawr by-pass.
Janette Ashfield handed the cheque to her local councillor Peter Read.
"This calls for a full and comprehensive look at the way Gwynedd Council finances are being managed," he said.
He added that the letter had now been returned to the council in the hope that it "will now be correctly addressed to its rightful recipient".
Ms Ashfield said she was concerned when she received the cheque.
"It's extremely worrying that such a large amount of money, owed to someone else, should find itself dropping through my letter-box," she said.
"That such a thing should happen demonstrates a degree of incompetence which verges on being irresponsible," she added.
Aled Davies, the head of the council's planning and transportation service, apologised for the "administrative error".
"We are already reviewing our internal procedures to ensure that a similar mistake does not happen again," he said.
"Of course, it should be remembered that any cheque is only payable to the individual whose name is printed on the cheque itself, therefore the person who received this cheque by mistake would not have been able to cash it."