The men did some work at the house and left without payment but returned soon after and dumped a skip full of soil and rubble on the drive, causing damage and blocking the path.
Another case involved an elderly female victim, who received a call at her door from three men asking if she would like some garden work done.
A West Yorkshire Police spokesman said: "The occupant agreed for trees to be cut and rubbish removed. A price for work to be done was agreed and the males asked for the money on competition.
"One of the males drove the occupant to the cash machine to withdraw money. Once paid, the occupant was dropped at her home address.
"She found they had dumped rubbish to the side of her garden prior to leaving."
Details of the two cases were shared as the force warned residents to be vigilant and to refuse workmen on the doorstep who offer to make repairs.
It said there had been a small number of bogus workmen targeting vulnerable people in west Leeds in recent weeks.
The spokesman advised residents to use reputable companies only and to get at least three quotes for the work.
Any suspicious incidents can be reported to police via the 101 non-emergency number or online here.