It did not take long after their daughter was born in December for Tiffany Score and Steven Mills, a Florida couple who had their baby through in vitro fertilization, to realize something was amiss, court filings show.

Ms. Score has blond hair and green eyes. Mr. Mills has light brown hair and olive skin. Their daughter looked decidedly different, with cocoa-colored skin.

A genetic test confirmed that the child had no genetic relationship to either parent. It turned out that another couple’s embryo had been implanted in Ms. Score, which she carried to term.

In the months since, many questions have been raised and few answered, but at least one sticking point appears to have been resolved with an agreement this month that Ms. Score and Mr. Mills will keep the baby.

The girl’s genetic parents have given up their claim to her, according to their lawyer, Rob Marcereau. (The couple have said they did not want to be named publicly, according to court filings.) The decision came after multiple meetings between the sets of parents, all of whom live in Florida, he said. The agreement allows the genetic parents to have contact with the baby, he said.

“As painful as this has been, they ultimately felt like this was the best outcome of a horrible situation,” Mr. Marcereau said. “There was no good answer. It was just agonizing for everyone involved.”

Mara Hatfield, a lawyer for Ms. Score and Mr. Mills, did not respond to requests for comment. In a social media post on Wednesday, Ms. Score praised their daughter’s genetic parents and said her family would maintain a relationship with them.

“While this chapter has brought more uncertainty and emotion than we could have ever imagined, this is the best outcome we could have hoped for, and our hearts are full of gratitude and relief as we look forward to moving forward as a family,” she said.

Ms. Score and Mr. Mills filed a lawsuit in January against IVF Life, Inc., the parent company of the Orlando Fertility Clinic, and Dr. Milton McNichol, who ran the clinic, which closed last month. The genetic parents are also planning to file suit in the case, Mr. Marcereau said.

Robert Terenzio, a lawyer for IVF Life, and Francis Pierce, a lawyer for Dr. McNichol, declined to comment, citing ongoing litigation.

In the court filling last week, Ms. Hatfield, the lawyer for the plaintiffs, said the embryo history of Ms. Score and Mr. Mills and other patients had revealed errors at the clinic that would support claims for damages. The couple is trying to determine whether one of their embryos was mistakenly implanted in another woman and is their biological child.

The case shines a light on what critics say is a lightly regulated, for-profit industry in which mistakes that carry devastating consequences occur infrequently, but still too often.

Proponents of I.V.F. say that at a time when infertility rates are increasing, fertility treatments allow a broad range of people to have children who would not ordinarily be able to to do so. The first birth through I.V.F. occurred in 1978.

OVU, a fertility matching website, estimates that the use of assisted reproductive technology has doubled in the last decade. More than 100,000 children were born last year through I.V.F., according to the American Society for Reproductive Medicine.

Mr. Marcereau, who said he is currently representing three clients who had mixed-up embryos from other clinics, said that cases of such errors are rare. “I wouldn’t say it’s happening left and right,” he said, but he added that “it’s happening enough that I see these cases popping up any year.”

In one study published last year in the Middle East Fertility Society Journal, an analysis of more than 400,000 cases of assisted reproduction showed an error rate of .58 percent.

Mr. Marcereau said the numbers of mix-ups are likely higher than publicly known since there is no reporting requirement for clinics and that in many cases parents welcoming a newborn child have little reason to think that it came from another couple’s embryo. A mix-up may be discovered only after a blood test or a genealogy test, he said.

In some cases, birth parents return the children to their genetic parents. That did not happen in the Florida case, in part because the law there gives greater protections to the birth parents, according to Mr. Marcereau.

Pam Belluck contributed reporting. Georgia Gee contributed research.