The original deadline was Friday, but officials moved it to June 5.
The extra time was necessary so the agency could consider additional medical information submitted by employees who want to remain at an alternate work site, said Teresa Cook, one of the affected workers.
The Choctaw resident said she still cannot approach the site of the 1995 bombing of the Alfred P. Murrah Federal Building without suffering a panic attack.
Cook said she is seeing a psychiatrist for another medical opinion in an effort to satisfy agency officials.
She said she doesn't expect that to help her avoid the agency's edict to move into the federal building, so she is willing to try it, if it comes to that.
At least two of her co-workers have opted for retirement rather than relocating, Cook said.