Controller calibration issues may occur at a few different levels.

Raw data level:
Any device with buttons, axis or feature that reports a state will report this through the USB stack. We define raw data as the data communicated to the operating system unfiltered. The only way to change the way the raw data reports is to run a firmware update on the controller if such an action is supported. Currently, none of the Flight/Space or Farm controllers in the Gaming has firmware updates available.

Windows level:
Windows drivers will add its own filter which we can think of as a layer on top of the raw data and this data is what you will see in joy.cpl, the test page of any device in Game Controllers.

The easiest way to fix bad calibration is to remove the controller’s Registry entry using the Registry Editor (RegEdit). See Recalibrate controller axes: RegEdit for more information.

Driver level:
Logitech drivers can add another filter on top of the Windows driver.  Typically these can be dead zones, response curves or other features added through the driver.

If the RegEdit fix did not work, try uninstalling the driver. See Uninstall A Logitech controller driver for more information.

Game level:
Games can add another filter level. Typically, dead zones or axes response curves (also known as sensitivity sliders). If the Game Controllers Test Page is reporting correct behavior but the controller is out of calibration in-game, then you may need to reset the game config settings. Follow these instructions to Recalibrate Flight Sim. 

For other titles, try looking on the developer's forum for guides on how to reset controller calibration.