Our state of the art Gantt chart
Try CSS. Check the DOM tree, main dialog has a CSS class
b-schedulerexportdialog, so if you need to apply your styling only into that dialog, use it in your rules.
background-color to manage color.
Same for buttons styling.
Another way is how to set some extra properties for the dialog and buttons is https://bryntum.com/docs/gantt/api/Grid/feature/export/PdfExport#config-exportDialog config.
Here is docs for https://bryntum.com/docs/gantt/api/Grid/view/export/ExportDialog with the list of names for all widgets inside. Export button has
Buttons has https://bryntum.com/docs/gantt/api/Core/widget/Button#config-cls config to set class.
All the best,