Generally speaking,the stories don’t tend to negatively impact the Doctor’s timelinein either direction.
Going back a little further, both men were once Jodie Whittaker’s Thirteenth Doctor.
This would be true for any Doctor that preceded Whittaker too.
Similarly,Fourteen would gain memories of a non-fatal encounter between Fifteen and a previous Doctor.
However, from a narrative perspective,it would actually benefit Fourteen to assist in future multi-Doctor adventures.
So, Gatwa could recruit Tennant to assist.
Custom Image by Daniel Bibby
Three Doctors are better than two, and Fourteen would understand that.
Therefore, Gatwa wouldn’t remember it either.
The latest Doctor Who series introduces the Fifteenth Doctor, joined by new companion Ruby Sunday.