I customized exported values for check-marks. But when I look at the exported .xml (.xls, .dbf) files, I see that check-mark values are exported as True/False. What should I do?

This issue occurs in case "Preserve value type on export" option is enabled in the export settings. This option results in exporting the default values and ignoring the customized values.

To resolve the issue disable  "Preserve value type on export" option in the export settings.