Given how easily she lied about her own father being dead, I'm sure that Paula won't have told the truth about Jac's dad. Also, given how feminist she was, I can imagine she'd be the type (especially in that era, early 70s) to have just used him as a sperm donor and decided that she didn't want any man involved and he had no rights at all, unless perhaps she needed money. From what Jac said, that was the only time they visited her Grandad.
I do think the likeliest explanation is that her biological father has been keeping tabs on her but believes that she doesn't want to know him (wouldn't put it past Paula to have destroyed any birthday cards, letters etc) or it is a foster father as we know she did have some - she wasn't in a childrens home the whole time.
You would think that after discovering what a liar Paula was though, re her Grandad and the sister, Jac might wonder how much of the truth she has been told about her father and investigate but maybe, as with Jasmine, she just feels it is too late.
I'm really glad they are readdressing the Surrogacy as I always thought they skipped over it too quickly though I do choose to believe that a reaction to it is the reason that Mo was a bit of a moo cow towards the end of last year - especially with Jac. Perhaps a subconscious resentment that Jonny wasn't able to spend as much time and care with her as she needed him most as she was getting over her loss because he was always preoccupied with Jac?