Every dental plan is different. Here in Canada with the Privacy of Information Act the insurance company cannot give any information via phone to anyone but the insured (you).
It sounds like you have a $1500 annual allowance for dental care with a $50 yearly deductible.
Your wife's dental surgery cost $900, the insurance was billed that amount. $50 was deducted from the $900 leaving $850 which the insurance paid $316.00 leaving $534.00 which the insurance did not pay. The insurance sent a cheque to the dentist for $316.00 since the $534 was disallowed because your plan with Delta has a cap on the amount they will pay per procedure.
If you have paid the dentist the full $900 and the insurance is only reimbursing you the $316.00, that is all the dentist has to give you back.
This should be a lesson learned, tough one though, ALWAYS, ALWAYS, ALWAYS ask the dentist to send a predetermination to your insurance provider BEFORE major treatment is done so you know exactly how much you will have to pay out of pocket.
Delta should be willing to provide you a copy of the cleared cheque. If you can't get the person you are talking to to agree to send it ask to speak to his/her supervisor and keep going up the ladder until you get what you are requesting.
I'm not quite sure what you mean by $500 write off. Who is writing the $500 off? Did the dentist agree to do that? (I find that highly unlikely knowing dentists like I do!