In a trademark dispute situation involving a figure as prominent as Tiger Woods, there are several things that could happen. First, either party could decide to take the dispute to court, where the legal process would determine whether any trademark infringement has occurred.
Both Tiger Woods (or his legal team) and the party disputing the logo have the right to provide evidence and argue their own case. In the court, it is necessary to prove that the new logo would likely confuse consumers, or that it is noticeably similar to an existing and protected trademark.
The court may order Tiger Woods to change the logo if found infringing another trademark, and could require monetary damages as well, depending on the level of harm established.
If they would like to avoid a legal battle, the parties could also try to reach an agreement through negotiation. This could involve modifying the contentious logo, or coming up with a financial settlement.
Legal advice from experienced trademark lawyers would be critical in such a situation, to make sure that all parties are respecting the trademark rights involved and acting in line with the relevant legislation.