This is the 16110th most frequent Russian word.
раздражающей
Irritating or annoying.
In this sentence, 'раздражающей' is an adjective referring to something causing annoyance or irritation, describing the voice.
Ее голос был настолько раздражающей, что я не мог сосредоточиться.
Her voice was so irritating that I couldn't concentrate.
Here, 'раздражающей' describes the effect of her manner of communication on him, indicating it caused irritation.
Он нашел манеру её общения раздражающей.
He found her manner of communication irritating.
In this case, 'раздражающей' modifies 'trait', indicating the characteristic was unpleasant to others.