I would certainly try to get this straightened out with the financial institution, but they tend to be reluctant to make any changes if the the Form 1099-R reflects the transaction that you requested, so don't be surprised if they leave you in the same situation that you are now. To be able to determine what the distribution of the particular dollar amount would have reflected if some or all of it would have been treated as a return of contribution requires reversing the normal calculation of Net Income Attributable based on account balances at the time of the contribution and the time of the distribution. Asking the financial institution to make a correction is actually a prerequisite to filing a substitute Form 1099-R (Form 4852).
Gain or loss is calculated over all of the investments in the account, so unless the entire account balance was held entirely in cash, it's likely that there was some investment performance needs to be taken into account. If there was truly no significant investment gain or loss in the account over that period, it might just be considered to be a de minimis error to ignore that gain or loss.
