The main booking.com speed dial on the start page is removable for me. I just right-click it and move it to the trash. Or, I can hover over it, click the 3 dots and move it to the trash. Or, I can goto the URL opera://bookmarks and remove it.
I don't have a booking.com one in the speed dial suggestions area.
If you see a booking.com thing above the main speed dial area, maybe it's something to do with the "Continue on booking.com" feature that you can disable at the URL opera://settings/startPage. But, as for the X you're looking for on the start page to get rid of it, the X might be a ways to the right of booking.com and it might be hard to see depending on your wallpaper.
On a side note, also notice the "Continue shopping" option in those start page settings.
Also note the promotional options at the URL opera://settings/privacy and the consent options at the URL opera://settings/privacy/consentFlow.