How did you add the image? I tried using html in the comments and you just saw the coding.
My Hebrew-speaking mum says that it should be pronounced "l'Pitriyah" and not "l'Fitriyah". Is she correct?
No, the rules say that the "dagesh" disappears once there is a ב/כ/ל/ו letter before it (indefinite form).
However, colloquially, almost everyone will keep saying the dasgesh, to make it clear that it is "<to a> Pitria". I feel that it would be quite difficult to find people that pronounce it according to the rules.
Sadly you need to learn to listen for both otherwise you'll be tripped up when it does happen.
This one comes up so often...i would love to compare a dog or a mushroom to something besides each other!