The biological parents of a baby born to another couple because of an embryo mix-up in Florida are doing their best to navigate an “absolutely impossible situation,” their attorney said.

Speaking days after the biological parents reached an agreement that allows the child’s birth parents to keep custody of the infant, their lawyer, Rob Marcereau, told NBC News that the last several months have been devastating for his clients.

“They are heartbroken over what has happened, and they also understand that the birth couple are also suffering,” Marcereau said. “They had to make the heartbreaking decision to not fight for custody.”

The baby girl, named Shea, was born in December to Tiffany Score and Steven Mills, a couple who had undergone in vitro fertilization at the Fertility Center of Orlando in Longwood, Florida. Score and Mills sued the clinic this year after testing revealed that Shea was not genetically related to either of them.

The revelation prompted a search for the couple whose embryo had been mistakenly implanted into Score, and in April, Score and Mills’ attorney announced that the biological parents had been found. The identities of the biological parents, referred to in court documents only as Patient 004, have been kept private.

The custody agreement will allow Marcereau’s clients to remain in Shea’s life, he said.

They care deeply about the baby and would have preferred to keep her as their own, Marcereau said, but it “would have been an incredibly uphill legal battle, and they just didn’t feel that that was going to be what was in the best interest of Shea.”

The decision came after several meetings with the birth parents, at which they shared “a lot of tears and hugs,” Marcereau said.

Score and Mills, who are white, pursued genetic testing on Shea because their baby “displayed the physical appearance of a racially non-Caucasian child,” according to their lawsuit. The testing revealed Shea was 100% South Asian, their attorney, Mara Hatfield, has said.

In a statement this week, Hatfield said Score and Mills have “begun and intend to continue to foster a relationship of friendship and trust” with Shea’s biological parents.

The clinic, which has since closed, did not respond to a request for comment regarding news of the custody agreement.

The extraordinary case has put a spotlight on IVF in the U.S., which experts say lacks oversight compared with other developed countries. Still, there is little precedent for such an extreme mistake: Embryo mix-ups are known to have happened to only a handful of families across the U.S.

Score and Mills’ lawsuit names both the fertility center and its lead reproductive endocrinologist, Dr. Milton McNichol, as defendants. The defendants have not disputed that Shea “should be, but is not, the genetic child” of the plaintiffs, according to a judge’s summary in court filings. McNichol did not respond to a request for comment this week.

Shea’s biological parents intend to sue the clinic and the doctor, Marcereau said.

“They have been placed in such a difficult situation that no one should be placed in, and the decision they have been forced to make has just been agonizing,” he said. “It’s just inexcusable.”