Eggsy had met up with Tilde before she went through the door to Chicago, for goodbye kisses (naturally) and to put a small tracker onto her so he could know if she was safe. He wasn't going to listen in on everything she was doing, he just needed to know if she got into trouble. Which didn't happen, of course. So he could honestly say he knew nothing about where she'd been.
He grinned when he got her text, and gave his suit one last look over before going through the door. He wasn't nearly as bad as Rox when it came to suits and clothes and things, but he did want to look good, and fit in. He lifted a hat and his luggage, and then headed through to Chicago to find Tilde's hotel. It wasn't difficult to find, so he detoured to pick up a bunch of flowers before going into the hotel. He was soon talking to the receptionist/concierge in his best Posh English Accent about how his beautiful wife had arrived the previous day while he was finishing up business in Detroit, and could he possibly get a room-key for their room? A generous tip was exchanged for a copy of the room-key, and Eggsy had made yet another new friend.
He went over to the old lift, a bell-hop carrying his suitcase behind him, and then they went up to Tilde's room. The bell-hop was tipped generously as well and then sent on his way before Eggsy knocked on Tilde's door.