With your project/model file open that currently exports the unwanted field names, go to the Options menu, and select Export and Clipboard... (assuming that you're still using v10.5 as your profile indicates). On the General tab, clear the check box which includes the field names as the first row of output. OK the dialog, save the model, and run the export again.
It should be as you need it now.
Does the bank take a CSV file for positive pay? We use Chase for positive pay and send them a csv file. Are you automating this with a batch script? You could have a second spreadsheet that has a module in it to open your exported spreadsheet and delete the first row. That macro could be called in the batch script.
It may be worth checking with the bank whether they need an Excel file or an Excel READABLE file. In most standard installation of MS Office that I am aware of a "CSV" type file, as suggested by Joey, tends to default to be an Excel file through windows file associations. This may have been changed, of course, for a specific machine/installation, but the default seem to be "CSV" > Excel.