The correct option is A The girl with grey eyes stole my purse and ran away.
An adjective phrase is placed after, or before the noun, it modifies.
From the
option, A has the correct placement, "with grey eyes" is the adjective phrase that modifies the noun "girl". Hence option A is correct.
Option B is incorrect because the adjective phrase has been placed at the end of the sentence, whereas it should be placed after the noun.
Option C is grammatically correct because it follows a noun "purse", but the sentence on the whole makes no sense as a purse does not have eyes.
Hence, option C is incorrect.
Option D is incorrect because the answer lies in A.