It is not unusual, when there is a dispute over admissability and evidence is excluded, for the attorney who had urged the admissability of the evidence to make an "offer of proof" for the record. This says, in effect, "If I was allowed to present this evidence, this is what it would be and this is what I think it would prove." That allows the appellate court to determine the relevance and materiality of the evidence if it concludes that the trial judge should have allowed it in.
Typically, the offer of proof is made at a sidebar conference or in the judge's chambers so that it is out of the hearing of the jury. I am assuming that if this was done in open court, it must mean that the jury is sequestered. Unless there is some gag order in effect (which is unusual) the press in the US are free to print anything that transpires in the courtroom. If the jury was not sequestered, the judge would have to assume this evidence would get back to them in some fashion.