What was Miss Mayela's real reason for inviting Tom into her house, and why is it important that Tom is right-handed? |

We do not know why Mayella Ewell really invited Tom Robinson into her house.  But the speculation is (what Atticus claims in court) that she had a very lonely life and she wanted to seduce Tom.   When Tom doesn't want to sleep with her, she claims he raped her.

The fact that Tom is right handed is important because all the bruises he supposedly inflicted on her are on the right side of her face.  A right handed man would have hit the left side of her face.

Her father is left handed...