The team found Mitchell told him they were from Princeton-Plainsboro Teaching Hospital and that Ben may need a transplant. He initially agreed to be tested, but when he learned they wanted to take him to another hospital for the test, he realized his ex-wife didn't want him to see his son and he refused.
However, it turned out Ben didn't need a bone marrow transplant and the doctors didn't have to pursue Mitchell.
When Ben became sicker, Janey's second husband Ron reached out to Mitchell so he could see his son before he died. However, Janey became enraged and insisted Mitchell leave. Mitchell resigned himself to leaving, but when he was walking away, House realized Mitchell had syphilis and that he had given it to Ben because he had molested him. That explained why Janey got so angry when he showed up, and didn't want him to be near Ben. They treated Ben for advanced syphilis and he improved quickly.