Question about removing vinyl flooring and replacing it with tile

I'm looking to remove the vinyl floor in my powder room and tile it. I've been watching tons of videos, but I'm confused about 1 part. In a lot of videos that remove vinyl there is typically a 1/8" hard board that gets pulled up with the vinyl. In my home (built in 2010) there seems to be a 0.25" hard board. Seen here: https://imgur.com/a/I3ffXok

If I am using Ditra under the tile, do I need to remove this hard board as well or can I simply put the Ditra over it? Removing this 0.25" hard board would make it lower than the adjacent hall/room.