Not saying how though for all those that want to find out themself.
But to all that already did, are you as disappointed as I am?
So I had to reload three times, letting my character with the best stats tackle it and then I succeeded in all rolls.
And then ' nothing ' of ' impact ' happened.

Ironically and by sheer luck I tried to open a similar object with a similar mechanic right away.
And when my first roll failed I noticed
that I have suddenly 3 more rolls to try!
So
THAT IS what was "in" the book?
Inspiration points?
I use the german client and I think there is some form of bug in that client, preventing me to see when I gain inspiration points.
From the Illythid at the start to whatever else gives us these points, I never see it when I collect any.
But gotcha: We get one for a slightly bigger feat or something, around this theme.
Even so - to have just reroll chances as a reward for something that looked like it might allow one of our partymembers to either become a Lich or gain knowledge towards the same, I don't dig. :|
Of cou~rse its just EarlyAcess

and the ultimate roll this book plays might still change, but... >exhales< ... inspiration points.
Oh well,
good enough for EA I guess. ¯\_(ツ)_/¯
Generally I think a re-roll should always come with the needed value halfed.
Because currently it feels like when the first roll was sh**, the second one will be even sh**tier.
And when this is not the case, it feels like the game tries to establish an Alibi or something.
Currently it really feels like the game is set on if your first roll sucks, so will the next one's.