If a neighbour reports television interference whenever you transmit, no matter what band you use, what is probably the cause of the interference?

When interference occurs regardless of the transmitting band, it indicates that the fundamental RF signal is so strong it is overwhelming the TV receiver's front end. This condition is known as receiver overload, where the sheer amount of energy causes the receiver's early stages to act non-linearly. If the issue were caused by deficient harmonic suppression or spurious emissions, the interference would usually only appear on specific bands where the harmonics mathematically align with the TV channels. The 'no matter what band' clue is the dead giveaway for receiver overload.