Opposition parties have reported Labour to the Electoral Commission after pictures circulated of West Yorkshire mayoral candidate, Tracy Brabin, handing out brownies with supporters tweeting their thanks.
Candidates are banned from offering sweeteners of any kind to voters under electoral law.
Labour has dismissed the complaints as a waste of the authorities' time, with sources insisting boxes of the cakes were 'thank yous' to party members for their hard work.
Police said on Tuesday night that no offence had been committed.
Asked about the issue while campaigning Pontefract on Wednesday morning, Labour leader Sir Keir suggested the claims were half-baked.
He said: "When I first heard this I thought it was a joke, that anyone would take this seriously.
"But Tracy's not offered me any brownies so I'm going to be talking to her about this later on!"
The Labour leader offered a ringing endorsement of Ms Brabin, and insisted he'd had a "positive reception" on the doorsteps of West Yorkshire while out campaigning alongside her.
The party is trailing badly in a number of national polls however, with the Conservatives widely predicted to win the Hartlepool by-election for the first time since the 1960s.
Sir Keir acknowledged Labour had "a mountain to climb" to win back voters who deserted the party at 2019 General Election, but added: "The poll that matters is tomorrow and we're fighting for every vote.
"People have actually been willing to hear from us and Tracy has been very popular on the doorstep because she talks common sense and they can see she's a champion for their community.
"Tomorrow is a very important staging post to elect candidates - mayoral and councillors - to be a strong Labour voice against this government."
Local Democracy Reporting Service