The force said that a joint investigation with the Population Office was under way into the activities of three UK companies.
Officers have urged islanders to check on elderly relatives, who may be “embarrassed” after paying “large sums” of money to the illegitimate firms.
The names of the companies are Next Up Roofing Contractors Ltd, Mayfair Roofing Contractors Ltd, and Diamond Roofing and Cleaning Ltd.
In a post on social media, police urged anyone who may paid for the services of these illegal traders to “get in contact”.
The post explained: “We understand that Facebook might not be the primary news method for the elderly in our community.
“Please check with relatives and friends to make sure that they see this message and haven’t been affected.
“Some people might be embarrassed about the large sums of money given to these companies, but we want to help and support you.”
If you have been affected, you can email hello@jersey.police.je or call 01534 612612.