Read the sentence. most castles no longer have original art, but each remaining noble still takes pride in heritage.

Most castles no longer have their original art, but each remaining noble still takes pride in its heritage.

Possessive adjectives are those adjectives that show a belonging relationship in an ample sense. In this case the first sentence uses their because it is talking about castles. In the second sentence it is better to use its because it is stating each which is singular.

Is aware that her tactics are not appropriate.

Explanation:

When Petrocelli states that the person must have lied, O'Brien objects to the statement. The most likely reason for the objection is that O'Brien believes Petrocelli does not have enough evidence to reach this conclusion. The fact that Petrocelli withdraws her question shows that she is probably aware that the tactic she just used is not appropriate.