An LGBT workplace rights advocacy group has launched an online petition to persuade a military contractor to adopt an LGBT-inclusive non-discrimination policy.

The change.org petition, created by Freedom to Work, is directed at DynCorp International LLC, a Fairfax, Va.-based company. The petition, which as of early Wednesday had 62 signatures, calls on DynCorp “to strengthen their non-discrimination policy by including sexual orientation and gender identity.

The company’s policies recently came under scrutiny in the wake of a settlement the company made with the Equal Employment Opportunity Commission over a case in which a straight employee,  James Friso, was allegedly subjected to anti-gay harassment and called “faggot,” “queer” and “dick-sucker” by a co-worker on a daily basis.

DynCorp allegedly did nothing after Friso complained about the harassment. As a result of the EEOC settlement this month, Friso will be awarded $155,000, but the company isn’t required to change its non-discrimination policy to include protections based on sexual orientation.

Tico Almeida, president of Freedom to Work, said his organization chose DynCorp as its first corporate campaign because of “explosive facts in the form of brutally ugly harassment” that were revealed after the settlement was reached.

“That kind of treatment is just plain un-American, and I think the public is going to have a visceral reaction that this company has to do better if they want to continue collecting billions of dollars in our taxpayer funds,” Almeida said.

DynCorp receives more than 96 percent of its revenue from federal contracts that amount to $2 billion each year, making it the 32nd largest federal contractor, according to Freedom to Work.

During a news conference Tuesday, White House Press Secretary Jay Carney didn’t have an immediate answer when asked if the administration has a problem with companies receiving this kind of federal money while not protecting employees from anti-gay bias.

“Why don’t I take that question because I know none of the details that you just described,” Carney said. “I don’t want to make a general statement about it since I know nothing about the specifics. But I’ll take the question.”

The White House didn’t immediately respond to a follow-up email request to respond to the question asked during the news briefing.

Ashley Burke, a DynCorp spokesperson, said in response to the petition, “we are currently examining our policies to determine how they can be further strengthened, including in this specific area.”

Almeida said he thinks persuading DynCorp to adopt an LGBT-inclusive non-discrimination policy is a “winnable campaign” based on the statement from DynCorp and because the company “is going to realize that discrimination is bad for the bottom line.”

“Most of the other military contractors like Raytheon, Boeing, Lockheed Martin, Northrup Grumman, and General Dynamics have already adopted LGBT non-discrimination policies, and many of them have specifically said that non-discrimination rules increase efficiency and make them a stronger and more profitable company,” Almeida said.

One way to prompt DynCorp to adopt an LGBT-inclusive non-discrimination policy would be for President Obama to issue an executive order prohibiting federal dollars from going to companies that don’t have sexual orientation and gender identity included in their policies. The White House hasn’t said whether Obama would be open to issuing such an order.

But Almeida said he’s “optimistic” Obama will issue the order early this year because it would fit with the White House’s “recent theme of governance.”

“He’s taken executive actions on politically charged topics like immigration, and he’s done things that have angered the business community such as mandating overtime payments for home healthcare workers and making recess appointments to the National Labor Relations Board,” Almeida said. “By comparison, the ENDA Executive Order is politically very easy.  ENDA polls very strongly with voters, including with a majority of Republican voters.”

The “ENDA” executive order is so named because it would be similar to the Employment Non-Discrimination Act, legislation that would prohibit workplace discrimination against LGBT people.

Almeida added the executive order could also be a component of a presidential campaign against Republican frontrunner Mitt Romney, who backed ENDA in 1994 but said he no longer supports the legislation in an interview in 2006.

“I think President Obama might even use his signature on the ENDA Executive Order as a wedge issue in the campaign against Mitt Romney, who has taken three or four different positions on ENDA, and to this day nobody knows what he stands for,” Almeida said.

UPDATE: The White House has responded to the Blade inquiry about companies receiving federal dollars without having LGBT-inclusive non-discrimination protections and the ENDA executive order with the following statement:

“President Obama has long supported an inclusive Employment Non-Discrimination Act and believes that our anti-discrimination employment laws should be expanded to include sexual orientation and gender identity,” said White House spokesperson Shin Inouye. “Regarding your question on a potential Executive Order, I don’t have anything to report.”