I like to think that Earth was The Doctor’s special interest planet as a kid. On the same level as kids being obsessed with the Titanic/ancient Egypt/ Greek mythology. Little guy just thought it was really fascinating.
They would’ve been so excited to see that their granddaughter was taking a liking to it too!
It also makes it way more fun to think about how they definitely knew the exact date of the end of the planet, not through their travels after leaving Gallifrey or the TARDIS helping them out with their date(?) idea, but because it was in some “entire history of the planet Earth” book they read cover to cover 30+ times when they were young.
Is it too much to ask for a fleshed out reference to the Doctor and the Master's time at the Academy? Not just "we grew up together" but "yeah we hated this class and always skipped so we could run amuck in the fields outside and dream of one day leaving together." Is it so much to ask for a reference to what the academy was like for them? Not just "we were friends in school" but "we had certain privileges constantly taken away from us since we blew up our labs so frequently." Is it so much to ask for a reference to the rock murder? Not just "one if our classmates just disappeared one day" but a full on flashback to baby Theta murdering Torvic for baby Koschei.