Headcanon:
Legolas doesn't know how or when his mother died. Nor does he know where. When he tells Tauriel his mother died at Gundabad, it isn't because he's lying but rather because that is how he believes she should have died. In battle, like a warrior. His imagination is all he has of her. He continues with 'there is no grave, no memory. Nothing.' to make up for the false fact he gave his friend.
Tauriel says nothing in return for it was the first time Legolas mentioned his mother.
Reasons behind this HC:
It's simple, it messes with my headcanon's of Mîlrin and how I painted her death before PJ dropped the Gundabad bomb.
I chose how Mîlrin died. It's painful, and I'm attracted to it. I'm not going to change it because the movie goes in another direction.