How can I increase the audio quality on Igel Thin Client?

For the audio quality on the Thin Client the integrated VC Framework VC is responsible.
Therefore, you should disable the audio hardware support.
There are several ways, depending on which Citrix connection you use:

1.  Session- Citrix XenDesktop/XenApp - Legacy ICA-Session- Sessionname- Optionen - Audiotransfer
2. Session- Citrix XenDesktop/XenApp - Citrix StoreFront / Web Interface - Optionen - Audiotransfer