The men gained entry to a house in Church Lane by saying they were police officers wanting to conduct a search.
Two of them rifled untidily through the upstairs rooms while the other stayed with the householder.
They then made off with a holdall, say Bedford police.
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The distraction burglary happened 8.45pm and 9.05pm on Wednesday 2 March.
Detective Constable Steve Wharton said: “We hope that issuing these images will lead to a possible identification of two of the suspects, or reveal new information, which could assist us in the investigation.
“I would also be keen to speak to anyone who witnessed any suspicious activity in the area at the time to get in touch.”
He added: “Impersonating a police officer is a serious offence, not to mention the distress and emotional toll caused to the elderly victim as these crooks violated her home.”
Anyone with information is asked to contact DC Wharton on 101 or call Crimestoppers, the independent charity, anonymously on 0800 555 11.