After learning of what happened to Amy Preston, Denise Christopher gave Lucy Preston a flash drive to Lucy containing as much information as possible about Olivia and Mark. This was so if they were somehow erased from the timeline, like Amy, she would be able to know, and not forget her children.
Mark makes his first on-screen appearance when Denise leaves to go to work. Upon arriving, she deduces that Rittenhouse has plans to erase her, and possibly her family from history. Seeing as there was nothing she could do to stop this, she decided to stay at the bunker and do some paperwork. Garcia Flynn, who has lost his family due to Rittenhouse lambasted her for this choice, and told her she should spend what was potentially the last remaining moments that her family had with them.
On the time travel mission, Lucy gives Denise Christopher the flash drive with pictures of her, Michelle, Olivia, and Mark. Lucy saves the Christopher family, as she promised to do in 2017.