Series first Vs Shunt First Filter Design
when the output impedance seen by the filter is greater than the input impedance, it is best to use a T-configuration (series first) filter.


No, this is not the case.

In a 'normal' filter, both terminations are resistive, you can use either a Tee or a Pi configuration.

When one of the terminations is designed to be either open circuit or short circuit, then you must use the correct configuration. Note the other termination of one of these filters must be resistive.

There may be practical reasons to choose Pi or Tee in a normal filter, whether it's between identical impedances or different resistive ones. Usually, we try to minimise inductors if there's a choice, as they tend to be bigger, more expensive, less 'ideal', available in fewer options, than capacitors. This means Low Pass filters tend to be Pi filters. The shunt Cs will often give us useful stop-band zeroes with their SRF, and you might as well have two of these rather than one. We might choose a Tee filter where it's intended as an isolating filter in a power distribution network, and the series elements are lossy ferrite beads. In that circumstance it's good to have HF power absorption on both sides of the filter.

Where the filter is intended to work into an open or short circuit however, the choice of Pi or Tee is forced. If one port of a filter is loaded with a short circuit, then any shunt component on that port is shorted, and so ineffective. A filter with a zero-ohm port, so driven from a voltage source, or into a short circuit, must have a series component to that port. 

Similarly a filter working with an open circuit, either a current drive or a high impedance load, must have a shunt component there, as a series component would be ineffective. This configuration often occurs when we have a large capacitance to drive at high frequencies, for instance a piezo transducer or a Kerr cell. We design a filter to drive an open circuit, at an impedance level where the final shunt filter C is bigger than the load C, then reduce the filter C to 'absorb' the load C into it.

An unexpected case of short-circuit operation occurs in the case of diplexers. Here, the common port maintains a constant voltage regardless of input frequency, so it is in fact a zero impedance point. The highpass and lowpass legs of the filter are then designed to work between a short circuit and the system impedance. As they are short circuit filters, they have series components on that port, which makes sense as those two ports are paralleled together to make the diplexer common port.