He discovered those unread messages when Race told him to check his old phone. Iñigo and Race accidentally met last a few days ago in a hotel abroad. Race was there for a business lunch while Iñigo will stay in that hotel for a few days.
Out of nowhere, Race asked him if he hates Cheska a lot. Iñigo planned to ignore Race at that time and leave him alone when he suddenly told him to check his old phone during college if he still has it. Race added in case that he already lost that phone, he will have something to regret for the rest of his life. After saying those words, Race left him and did not try to talk with him again.
That really piqued Iñigo's attention. Fortunately, he still has his old phones with him and some of them are still working. The words Race told him that day kept on ringing in his ears that's why he decided to follow his instruction. And besides, he knows that Race will not tell him those words for anything.