It might be obvious to one who has absolute pitch. But if the whole piano is out by that quarter tone, the majority of people would not notice. Unless they played along to a recording that was at concert pitch. It may have been tuned thus on purpose. If it's only certain notes, or one string out or two/three, then it's a different matter. But if it's in tune with itself, let sleeping dogs lie.
You will need certain tools, the hammer being crucial - use the wrong size, and you could end up wrecking the pegs. You won't be able to use a tuner, like you would with a guitar. It's often a few hours for an experienced tuner to pull up a piano, so I believe it's a bad idea for you to attempt this.
If it was my piano, I wouldn't let you near the inside, and would question the mindset of grandparents who are happy for you to experiment on their pride and joy.