The correct option is D NO CHANGE
The underlined word 'theirs' is a possessive pronoun that means 'it belongs to them'. 'Theirs' is correct here as it refers to the money that the 'grandchildren insist on possessing/owning.
So, there is no change required and option D is correct.
Option A: The pronoun 'theirs' does not use an apostrophe. The idea that pronouns like 'her, his, their' use an apostrophe arises from the fact that an apostrophe s ('s) indicates possession. But, these words do not indicate possession using the 'apostrophe', they only require the 's'.
Hence 'their's' is grammatically incorrect and option A is wrong.
Option B: 'They're' is a contraction of 'they are'. These words do not indicate possession (of money). 'They're' will be followed by a participle, or an adjective; e.gs, 'they are coming today', 'they are ready'.
Since there is no participle or adjective that follows, option B is incorrect.
Option C: Similarly, 'there's' is a contraction of 'there is'. It does not indicate possession, but introduces a clause or a sentence. For example, 'there is a storm going on outside'.
Hence option C is also incorrect.