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Hi and welcome to JustAnswer, I’m Louie. Sorry you had to wait awhile but I’ll do my best to help.Initially, is the described issue of "...can't hear them..." even if using the corded handset of the base unit?
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Are you able to:
"...yes..."? ...able to listen to both messages left and greeting message?
Then it would appear that there is no issue with the Panasonic phone.
Do you have a spare / conventional corded phone?
Still, have you brought this to the attention of the land line / home phone service provider?
Are you able to call them using a cellphone?
The MUTE works so that the caller does not hear you.
Other than the VOLUME ▲ button, there is no other control that can cause the caller's voice not to be heard.
That you can hear the "Greeting Message" is indicative that the Panasonic's audio/speaker system is operational.
By process of elimination, this then leaves us with the phone company as the most likely cause.
A way to confirm would be to temporarily replace the Panasonic with a spare / conventional corded phone.
Still, it would be to your advantage to inquire/inform the phone company.
Also try to call the Panasonic phone using your cellphone and leave a message. This would be a test of the caller's messages / "...not really sure on the answering machine..."
Is further information/assistance still needed with this Panasonic?