Is it permissible for a girl to inform her father that the suitor has purchased the required quantity of gold, when in fact he has bought less, due to the father's exaggerated financial demands?

Marriage without a dowry is not permissible for anyone other than the Prophet (peace be upon him). Therefore, a dowry is obligatory, even if it is small, or a recognized benefit such as teaching the Quran. Islam encourages facilitating marriage, and a woman may forgo whatever she wishes of her dowry after the marriage contract, or give all or part of it to her husband, as Allah Almighty says: "And give women their dowries as a free gift; but if they, of their own good pleasure, remit any part of it to you, take it and enjoy it with good cheer." There is no blame upon the questioner for forgoing part of her dowry. If the gold is not part of the dowry, then it is permissible a fortiori. She may also use allusions with her father, such as saying: "The requested gold has been bought," meaning what is requested by her. Indeed, allusions suffice to avoid lying.