Use 'their' when showing possession, 'there' for indicating place, and 'they're' as a contraction for 'they are.'
Their is a possessive pronoun, there indicates place, and they're is a contraction of 'they are'.
For the sentence provided, the correct homophones to complete it are their, there.
Example: 'They forgot their keys over there,' meaning the keys are in that place.
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