Third Party Pledge on loans secured by CD

I hate asking this question ...but I am in a quandry and need some advice. Here is the situation:

CD owned by "A" and "B" (Joint tenants with rights of survivorship)

"A" comes in and takes a loan with the CD as collateral.

Does "B" need to sign a Third Party Pledge Agreement?

I believe we would have "B" sign the Third Party Pledge to perfect our interest in the collateral.

It is our practice to get this done; however, I am getting some STRONG pushback from the new "powers that be." They would like to see it in writing, blah, blah, blah.

Can someone give me guidance?????

Some of this may be influenced bt state laws. As a general rule, if A or B could cash in the CD either can obligate it. (In Texas) A notice may then be sent to the other advising them of the pledge as collateral and they can duke it out if need be.