For the service in question, try setting DTMFMethod to InBand (this may degrade outbound DTMF reliability, e.g. when accessing IVR systems).
Or, try changing DTMFPlaybackLevel for the Phone port from -15 to e.g. -60. (If that helps, it won't eliminate the beeps, but should make them much softer.)
If no luck, please post: Do you have the problem with both GV and VT? Calling both her mobile and her landline? Who is her landline provider?