I have quite a few locations ESI-Linked and remote phones or a combination of both. The systems I have work fine and the only time I have ever experienced a "Voice Quality" problem is when the internet has had issues.
We use the internet which in most cases is not as good (public network) as what you have (Point to Point T1)

Use the link below for a more in depth test of your connection. Keep in mind that this test should be done while you are experiencing the problem. Run the test multiple times.

https://www.voipreview.org/voipspeedtester.aspx

When you say sound quality is "poor" what do you mean??????

Do you hear echo? are calls getting dropped? Is there a volume problem??

Are phone conversations at the host good, or are they too poor?

What are you using at the host for dial tone? (SIP, POTS, PRI T1, or dial tone provided via the internet like a cable company)

I bet you have a bandwidth problem.
If calls are good at the host you can eliminate the card that interfaces to your dial tone service(PRI card, SIP card or Analog trunk card)

If the Point to Point T1 checks out, the next thing I would do is replace the IVC card.

This problem is definitely fixable, and identifiable, you just need someone that has the experience to trouble shoot this.

If you provide more info, I can help you figure out the problem.

Walter