Limited-overs captain Hope has played 38 Tests, the last of which came in Sri Lanka in late 2021.
The CWI said veteran all-rounder Jason Holder turned down the offer to join the squad in India to undergo a pre-determined "medical procedure".
Tagenarine Chanderpaul and Alick Athanaze were recalled in the West Indies' 15-member squad for the two-Test series in India next month.
Mitchell Starc delivered the fastest five-wicket haul in Test history on Monday as Australia crushed the West Indies by 176 runs in the third Test in Kingston, Jamaica, to complete a 3-0 series sweep.
Assessing Sai Sudharsan's temperament and Nitish Kumar Reddy's utility in home conditions would be topmost on India's checklist when the high-on-confidence hosts take on a floundering West Indies
The West Indies produced another dominant day with the ball against Australia and then survived a tense final hour Saturday to take the honours after the first day of the day-night third Test.
The short turnaround time from the high of winning a controversy-marred Asia Cup notwithstanding, Shubman Gill's India will be outright favourites against a struggling and under-strength West Indies when the teams face-off on a green-top in the first Test in Ahmedabad on Thursday.
Speaking ahead of the first Test from June 25 onwards at Barbados, Joseph said as quoted by Sydney Morning Herald, "To take 13 wickets across the series was a good feeling. A lot has changed. There were a lot of opportunities that came my way."
Kristian Clarke (4/25) first shone with the ball to restrict the West Indies to 238 and then scored an unbeaten 46 off 42 balls to take New Zealand home in the company of Joey Field, who was not out on 38.
Nyeem Young was named man-of-the-match for his all-round show to help the West Indies register their second win in as many matches.
