$0.22 NLHE MTT Deep Stacked: set on a straight turn

PokerStars - $0.20+$0.02|100/200 Ante 20 NL - Holdem - 9 players
Hand converted by PokerTracker 4

SB: 40.14 BB (VPIP: 12.24, PFR: 2.08, 3Bet Preflop: 0.00, hands: 51)
BB: 48.43 BB (VPIP: 9.52, PFR: 0.81, 3Bet Preflop: 0.00, Hands: 127)
UTG: 45.93 BB (VPIP: 20.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 10)
UTG+1: 15.68 BB (VPIP: 31.25, PFR: 25.00, 3Bet Preflop: 25.00, Hands: 16)
MP: 116.64 BB (VPIP: 50.00, PFR: 6.67, 3Bet Preflop: 0.00, Hands: 16)
MP+1: 41.31 BB (VPIP: 37.50, PFR: 12.50, 3Bet Preflop: 0.00, Hands: 16)
Hero (MP+2): 38.65 BB
CO: 50.39 BB (VPIP: 18.75, PFR: 12.50, 3Bet Preflop: 0.00, Hands: 16)
BTN: 52.36 BB (VPIP: 37.50, PFR: 12.50, 3Bet Preflop: 11.11, Hands: 16)

9 players post ante of 0.1 BB, SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 2.4 BB) Hero has 8<font color='red'>♦</font> 8<font color='black'>♣</font>

fold, fold, fold, MP+1 raises to 2.24 BB, Hero calls 2.24 BB, fold, fold, SB calls 1.74 BB, fold

Flop: (8.62 BB, 3 players) T<font color='black'>♣</font> J<font color='black'>♣</font> 9<font color='red'>♥</font>
SB checks, MP+1 checks, Hero checks

Turn: (8.62 BB, 3 players) 8<font color='black'>♠</font>
SB checks, MP+1 checks

what to do here?

check. and river check/fold unless board paired

I agree, check behind and be done with the hand unless the board pairs.

I think it's unlikely to get paid getting paid by 1 or 2 pair hands with a 4 straight and flush draw on the board. It's possible some 7s would fold the sucker end of the straight so maaybe...

Betting the turn here is a bluff imo.

Check it back, hope the board pairs on the river. You still have some showdown value and no worse hands are calling a turn bet.