What does the word “hard” convey?

The word hard conveys the idea of being strong, severe, harsh. The Israelites have not exercised any constraint in their criticism of the Lord. They have spoken words that have severely offended the Lord. The three words (words, hard, and against) form an idiom that conveys the idea of the words of one speaker prevailing over the words of another speaker (see 2 Samuel 24:4). For this idiom to apply in this verse, we would need to envisage a contest of words between two speakers, one prevailing against the other. That is, the words of the Israelites are prevailing against the words of the Lord. This is possible, but the text does not speak of such a contest of words, as in 2 Samuel 24:4 (where Joab is contesting the command of King David).