Hi, Alexander.
As you are suspecting, this is most likely a codec-mismatch issue, with your IP phone set to use g.729 (that's what the "Optimize for low bandwidth"
option does), and some component of your Contact Center solution (perhaps UCCX or IPIVR) configured for g.711.
So it becomes a question of properly configuring the transcoding ...
If you can't find more assistance with transcoding on this forum, you might want to try the IP Telephony forum:
https://supportforums.cisco.com/community/netpro/collaboration-voice-video/ip-telephony
Good luck!
-Paulo