Final answer:
The word that best fill the blank in 'I saw them over ________ in the park having a picnic.' is 'there', as it indicates a location in the park. 'Their' and 'they're' do not fit in this context.
Step-by-step explanation:
The correct word to fill the blank in the sentence 'I saw them over ________ in the park having a picnic.' is there. 'There' indicates a place, which fits the context of the sentence. Unlike 'there', 'their' is a possessive pronoun which would not make sense in this instance, and 'they're' is a contraction of 'they are', which also does not fit the context of describing a location in the park.
It's important to differentiate between these homophones: 'their' refers to something owned by them, 'there' refers to a place, and 'they're' is short for 'they are'. For example, in the sentence 'The Smiths rescued their missing cat from that tree over there; they're happy to have him back,' each homophone is used correctly according to its meaning.