What should be the first step to resolve non-fiber optic cable TV interference caused by your amateur radio transmission?

Interference to a closed cable TV system from an amateur radio transmission is almost always caused by a breach in the RF shielding of the cable network. The coaxial cable used by the provider is designed to keep their signals inside and your radio signals outside. The most common points of failure in this shielding are loose, corroded, or improperly installed coaxial connectors. Therefore, the very first and easiest step is simply to check and tighten all the physical connections on the TV feed line. Adding filters is generally ineffective for closed cable systems, and a preamplifier would just amplify the interference.