To effectively make a telephone hybrid work, the studio end of the conversation should originate on a studio microphone . You can feed the studio microphone audio through one input of a mixer and use an aux buss to feed the telephone hybrid. Your audio output from the hybrid is connected to a second mixer input and is NOT fed back through the aux buss. You can then mix the two separate inputs to suit or record them to separate tracks to mix later. You may wish to add a compressor to the caller input to help stabilize the volume variations as you would any other microphone.
Some additional equalization can also be helpful.
This can also be set up with a gate if you have the time to set all the adjustments. Obviously if the mixer and the studio talent are not one in the same, some degree of coordination will be necessary. If you do not use a mixer, then you will be depending on the quality of the hybrid for your two sided conversation recording. Some other thoughts. Many businesses today may use a lower quality bulk line for their long distance calls.