The national chain, based in Langholm, is accused of committing the offence on two occasions in 2014.
A trial began at Dumfries Sheriff Court last month but reporting restrictions prevented publicity.
Lawyers for the company argued it could have affected witnesses and voiced concerns about the business impact but the ban has now been overturned.
The alleged offences, brought under the Textile Products Regulations 2012, are said to have taken place at the company's store in Church Place, Dumfries, one of 265 high street shops.
When the trial  began at Dumfries Sheriff Court on 15 September, Susan Duff QC, for the accused, argued against an application on behalf of the BBC and ITV Border to revoke the ban, arguing that publicity could affect the evidence of witnesses who are yet to come to court.
She also said: "The accused has a legitimate concern about its business and employees.
"Now is the busiest time of year for the purchase of cashmere."
She said reporting that scarves were not 100% cashmere could be "prejudicial to the legitimate interests" of the firm.
But Ronnie Clancy QC, for the BBC, argued that this being "the busiest time of year for Christmas orders" was simply a reputational issue, not covered by the Contempt of Court Act under which the ban was made.
Sheriff George Jamieson agreed to revoke the interim order he had previously made, and allowed the case to be reported.
Previously, Alison Irving, 52, a trading standards officer at Dumfries and Galloway Council, told the court she had test purchased a blue tartan scarf in February 2014 and a red one four months later.
Both scarves were reduced to Â£30 from Â£60 and were labelled as 100% Lochmere cashmere, the court heard.
Ms Irving later cut the scarves into pieces, bagged and sealed them and sent them off to be analysed at two different test labs - SGS UK and Intertek UK.
It emerged that she was acting on information from the Cashmere and Camelhair Manufacturers Institute (CCMI).
On receiving reports back from the test labs, Ms Irving said she sent a letter in August 2014 cautioning EWM.
She said she notified the business that one scarf had been found to contain 84.4% cashmere, while the other was found to have 61.6% cashmere, with the remainder made up of other wool fibres.
Under cross-examination from Ms Duff, the witness said it was "odd" that the results received back from each of the labs had been different from each other.
"They were different from each other but neither said they were 100%," she said.
The witness confirmed that after sending EWM a sample, the company sent back results from another test lab showing that both scarves were found to be 100% cashmere.
Ms Duff also challenged the evidence of a textile analyst Liqin Zhang who gave evidence saying she identified wool and yak in the scarf samples.
Ms Duff told Ms Zhang that EWM had sent a DNA tested 100% cashmere sample for her to analyse in August 2016.
The lawyer said the fabric had been subject to the same processes and dyed the same colour as the red scarf sample previously tested.
Ms Duff told Ms Zhang: "You identified that 100% cashmere sample as 85% cashmere and 15% unidentifiable fibres.
"The issue is with your identification and not with the product, isn't it?"
Ms Zhang replied: "If the fibre structure is damaged I have to report it as unidentifiable, I can't just guess."
Ms Duff continued: "You couldn't identify fibres that were 100% cashmere, that's down to your ability?"
Ms Zhang replied: "That's my decision on what my observation is. I'm not saying I'm perfect."
The trial continues.
Edinburgh Woollen Mill has denied a charge of mislabelling scarves as 100% cashmere in a store in Dumfries.