Just re-watched the episode and got to the part where Jeoffrey was giving Jaime a hard time about his legacy only being half a page in the book of brothers and paused it to read what the page said.
Ser Jaime Lannister
Squired for Barristan Selmy against the
Kingswood Outlaws. Knighted and named
to the Kingsguard in his sixteenth year for
valor in the field. At the Sack of Kings's Landing
murdered his king, Aerys the second, at the foot
of the Iron Throne.
Pardoned by King Robert Baratheon. Thereafter
known as the Kingslayer.
That's what was written in the brothers book for his legacy. That's some tough shit to deal with especially when you know the truth to be much different then what everyone else believes.