We want to help, but you will get more questions here than answers, unless we can get more info.
We have spoken before, I believe, about a similar situation. Please see my remarks, and those of other forum members, in the referenced thread, from May of this year. At that time, we recommended that you avail yourself of the services of a professional installer. Personally, I would say that that advice still stands.
archives What is the name and model number of the recording equipment? What wiring scheme is recommended by the manufacturer? Do you see the letters "RJ" followed by other letters or numbers on the installation instructions where it talks about interconnecting to a phone system?
If you are the company who installs the equipment, why aren't you familiar with the way the wiring impacts on the customer's equipment? Are the "wiring people" (whatever that means) licensed electricians with specialized telecommunications training?
What does the customer (or what do you) ask the "WP" to do? Are they installing some sort of wiring or jacks that inserts a series connection between the phones and your equipment?
You first ask about a brand-new installation where the phones stopped working. When that happened, did the "WP" stop what they were doing and analyze and correct the problem? If, one minute, phones are working, and then, right after someone meddles with the wiring, all the phones stop working, I would be concerned that the "WP" might not know what they're doing, or to be charitable, perhaps they have not been instructed properly as to the consequences of their actions.
Did the phones start working again? Who did what to get that to happen?
Then you ask about a scenario where you might be required to remove, at least electrically, your recorder, and wonder whether the phones will continue to work. Has that ever happened before? Does the manufacturer offer any advice or instructions that would guide you in that eventuality? Can you give us a hint as to what the instructions say? How many of these installations have you had done?
I have been working on phones for 45 years, and I have never heard of a term in telephony called "reflection." Please have your manufacturer explain what that means, and then relay the information to this forum.
If your company does not have the expertise to do these installations yourself, then my suggestion would be to hire a telecom professional to work for you directly, as a subcontractor, on these installations. They should fully acquaint themselves with the wiring requirements before meddling with a customer's equipment.
Oh...wait...that's what I said last time.