In this case I think I would translate this as "Who has the pear?" because, although "ta hruška" means "the pear, that pear" being both interchangeable, in this case it doesn't makes too much sense to ask for "that pear", because it sounds like your pointing to "that pear" placed there. Is it right? Or I missed something?
‘Whose is that pear’ sounds better. I’ve never heard anyone use the phrase ‘who has that ...’
Maybe it sounds better, but it is not the same sentence. ‘Whose is that pear’ - is "Čí je ta hruška."
I thought exactly the same, I had to ask a native speaker to explain this. It doesn't actually mean "Whose is that". There is a specific pear the speaker wants, which someone has. So, "Who has that pear" is actually accurate.