A newly filed civil case alleges a fertility doctor secretly substituted his own DNA during treatment, resulting in the births of two girls.
"Mr. Vance, I pray that your daughter is fortunate enough to bear children of her own one day," Aniston wrote.
Meanwhile, births continued to shift to older mothers.
Alabama has a new law protecting in vitro fertilization providers from legal liability.
Republican Sen. Cindy Hyde-Smith of Mississippi blocked quick passage of a bill on Wednesday afternoon that would have enshrined protections for in vitro fertilization and for the doctors who perform the procedure.
Alabama House Democrats introduced a bill Thursday that would establish that fertilized human eggs stored outside of a uterus are not considered human beings under state law.