What is the meaning of this quotation in She Stoops to Conquer? Hastings: If she succeeds, it will be the most delicate way at least of obtaining them.
In Act 3 of Oliver Goldsmith's She Stoops to Conquer Hastings meets and quickly falls in love with Constance. Constance is already being pushed to marry Tony, who is Mr. Hardcastle's stepson only because Constance has a casket full of very valuable jewelry and Mrs. Hardcastle wanted it.
As a result, Hastings proposes to elope with Constance who, now, would have to find a way to get her jewels from the hands of Mrs. Hastings. Since Tony does not want to marry Constance anyway, he even tells Hastings that he will help with the plan to get the jewels and with the elopement.
Therefore, Tony used his usual tricks to get the jewels, sent them to Hastings, but did not explain how he got them other than
If I had not a key to every drawer in mother's bureau, how could I go to the alehouse so often as I do? An honest man may rob himself of his own at any time.
At this time, Contance is asking Mrs. Hardcastle permission to wear her jewels because he had no clue that Tony and Hastings were planning this. Hastings knows this and also knows that it would be nearly impossible to get those jewels from Mrs. Hardcastle without any issues. This is why he says
If she succeeds, it will be the most delicate way at least of obtaining them.
In other words, that would be taking the "nice" route rather than having opened the drawers and flat out stealing them from their original location like the two men did.