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The only two river lines that make sense here (in my mind) are check-call or bet-fold. If you're going to call a raise, you're better off just check-calling.

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I agree with this. FWIW, from the get go I thought it close.

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I challenge those who think this is a bad bet-fold

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I do a bit of work to support my assertion that c/c is better then b/f.

The following is subject to change given your image and you can dispense with or include ones that I miss:

For c/c to be better then b/f he needs to bet w/ more beaten hands when checked to then beaten hands he would call with. Since it is always 1 BB to showdown all hands villain raises w/are null.

Range at river decision to bet or check:
55,88-TT = 21 hands (JJ?)
A7-AQ = 40 hands (no AT)
Kxd,Qxd,Jxd plus some S.C. ~ 32
89s not d – 3

Assumptions for villain:
at least calls with all Ax hands and all PP
bets all A hands
Raises suited and maybe AQ, AJ

Hero is ahead of A8-A9 – 16
Behind A7, AJ, AQ – 24

16 betting when checked to
Vs.
21 checking behind

In a 6BB pot 16 hands is worth 16/96 * 6BB ~ 1BB
In a 5BB pot 21 hands = 21/96 * 5BB ~ 1.1

So, b/f is only better by a tenth of a BB if villain never bluffs. Villain only has to bluff ~1.5 hands (1.6%) of his hands to make B.E.

Thoughts? Corrections? Omissions?