Shake Shack has returned a $10m loan it received from the US government as part of a small business emergency funding programme meant to ease the damage done by coronavirus lockdowns.

The burger-and-hotdog chain restaurant was one of the recipients of the Paycheck Protection Program, which is a $349bn stimulus package aimed at helping small business owners keep their employees.

The stimulus money – which has already been exhausted – was managed by the Small Business Administration.

The fact that large hotel and restaurant chains, as well as publicly traded companies, were able to apply for the PPP stimulus sparked a wave a criticism in the days following the funds' dispersal.

"Large restaurant chains, including Ruth's Chris steak houses and Potbelly sandwich shops, dipped their snouts in the trough and got millions in aid. The program was meant for small businesses. A last-minute loophole was scribbled into the bill on their behalf," New York Times columnist Jennifer Senior wrote.

Main Street Alliance, a network of small business owner coalitions, wrote that the "#PPPloan suffers from design flaws-money should be distributed by the Treasure Department, perhaps in partnership with local or state governments, instead of banks + #smallbiz should be given #grantsnotloans."

US Rep Alexandria Ocasio-Cortez compared the ease at which the $4 trillion corporate bailout was rolled out to the execution of the PPP stimulus.

On Monday, Shake Shack's CEO Randy Garutti and chairman Danny Meyer explained in a letter posted to LinkedIn why they decided to give the money back.

They said that they chose to return the funds after learning the PPP money had been exhausted, and determined the money was likely needed more by smaller restaurants.

"Shake Shack was fortunate last Friday to be able to access the additional capital we needed to ensure our long term stability through an equity transaction in the public markets. We're thankful for that and we've decided to immediately return the entire $10 million PPP loan we received last week to the SBA so that those restaurants who need it most can get it now," Mr Garutti and Mr Meyer said.

In the letter, the executives explain why they applied in the first place, and how they came to be increasingly confused by the rationale guiding the allocation of the money by the SBA.

"With the country facing a prospective permanent loss of restaurants up and down the food chain, the bill arrived just in the nick of time. The onus was placed on each business to figure out how, when, or even if to apply," they said. "The 'PPP' came with no user manual and it was extremely confusing ... the best chance of keeping our teams working, off the unemployment line and hiring back our furloughed and laid off employees, would be to apply now and hope things would be clarified in time."

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The executives explained that while "the program was touted as relief for small businesses" they also learned that it would provide funding for "any restaurant business – including restaurant chains – with no more than 500 employees per location would be eligible."

As they note, there are few, if any, restaurants in the country that employ more than 500 people per location, effectively opening up the PPP, which is aimed at small businesses, to every chain restaurant in the country.

"We cheered that news, as it signalled that Congress had gotten the message ... restaurants needed to survive. There was no fine print, anywhere, that suggested: 'Apply now, or we will run out of money by the time you finally get in line,'" the letter said.

They said that since Shake Shack met the criteria – the company employs approximately 45 workers per location – that it made sense for them to apply for the money. They describe losing more than $1.5m weekly due to the drop in business and admitted that Shake Shack and parent company Union Square Hospitality Group have had to lay off or furlough "hundreds" or – in the latter's case – "over 2,000" employees.

The executives called on Congress to pass more effective funding measures to help restaurants of all sizes while people are on lockdown due to the coronavirus.

"While it is heartening to see that an additional $310bn in PPP funding is about to be approved, in order to work for restaurants, this time we need to do it better," the letter said.

Mr Garutti and Mr Meyer called on Congress to fund a new stimulus package "adequately," saying that "it's inexcusable to leave restaurants out because no one told them to get in line by the time the funding dried up. That unfairly pits restaurants against restaurants."