The St Helens Labour Party group, which lost all but two councillors in the election, said it was “deeply concerned” about Reform’s vetting procedures.
“Being elected as a councillor is a position of public trust and responsibility,” a spokesperson said.
“Political parties have a duty to ensure that those standing for office meet appropriate standards and are fit to serve their communities.
“This latest controversy raises wider concerns about Reform UK’s ability to put forward credible, properly vetted candidates capable of representing residents seriously and responsibly.”
Merseyside Police was called to Perry’s Bar, on Duke Street in St Helens, at 01:30 BST on 6 April last year to reports a woman in her 60s had been pushed over outside the bar.
Beck later attended a voluntary interview and was charged.
She denied the offence but was found guilty at South Sefton Magistrates’ Court in Bootle on 15 January following a trial.
Her sentence was a £180 fine, alongside an order to pay the victim £100 in compensation.
Only criminal convictions that attract custodial sentences of more than three months prevent candidates from standing in local council elections.
Beck is the third newly elected Reform councillor in Merseyside to face questions since polling day.
Jay Cooper, who won a seat on Sefton Council representing Bootle West ward, resigned from the party after the elections over social media posts appearing to claim that the Holocaust was a “hoax”.
He then retracted the comments, saying he was “not denying the existence of the camps or the systematic murder carried out by the Nazi regime”.
Then last week Stephen Mousdell, who was elected to represent Haydock ward on St Helens Council, triggered a by-election by resigning when it emerged he had posted explicit pornographic content on social media and the adult content platform OnlyFans.
Mousdell had been backed by Reform, and there was no suggestion of any illegal activity, but he posted on social media that the “immense pressure” he and his husband had faced was affecting his mental health.
Nigel Farage was questioned over the vetting of new councillors, specifically in reference to Cooper, on a visit to St Helens on election results day.
He told the Liverpool Echo newspaper: “When you are putting up 5,000 people, do some slip through the net because they don’t tell you their social media handles or tell you the truth? Yes. Do we welcome people with these ideas?
“No we absolutely do not.”
Emma Beck and St Helens Council have been contacted for comment.