Former players and media pundits have pushed for master batsman Smith to be reinstated, and called for 36-year-old Paine to step aside after a shock 2-1 loss to a severely depleted India in the home summer.
Australian pace bowler has Andrew Tye left his franchise Rajasthan Royals for 'personal reasons'.
The Kerala wicketkeeper-batsman was picked up for his base price of Rs 20 lakh in the IPL auction last month.
A total of 292 cricketers are set to go under the hammer on Thursday.
Chennai Super Kings retained veteran Suresh Raina, while the explosive Glenn Maxwell and opener Aaron Finch were released by Kings XI Punjab and Royal Challengers Bangalore respectively.
India, chasing 328, were 4/0. The hosts must win the match to claim the Border-Gavaskar Trophy while India need only a draw to retain the silverware.
Australia exploited India's injury woes and punished their poor fielding to reach 274/5 at the close of a steamy opening day of the fourth Test.
Video footage from the stump camera of Smith dragging his boot across the crease on a tense final day of the match went viral on social media and some former players accused him of gamesmanship at best, cheating at worst.
The Indian all-rounder produced a moment of sheer brilliance to prove why he is considered one of the best fielders in contemporary cricket.
Smith insisted he has no issue with the quicks bowling short to lower order batsmen.