Roy, W7EL wrote:
"Then does the "reflected power" flow back out, to go back down the
transmission line, or does it contribute to the load dissipation?"

It is a matter of time. Eventually, the reflected power is consumed by
the load, though some of it requires several attempts to make it through
the load.

The load impedance opposes alternating current and thus the power it can
produce.

Reflected power is a misfit in the load. It does not conform to the E /
I ratio of the load. There is a surplus E or I when there is a mismatch.
This surplus E or I is reflected initiating the reflected wave traveling
back toward the transmitter in the Zo of the line. E / I of the
reflected wave must be the same as Zo enforces on the incident wave. Zo
is usually a resistance (Ro) in useful lines. Zo is nearly the sq. rt.
of L/C in useful lines because their series resistance and shunt
conductance are insignificant. In such lines, Ro is lossless.

If the transmitter is matched to the feedline to deliver maximum power,
no reflected power gets through the matching network. This means that
all reflected power is re-reflected by the network.

So, the incident power consists of the transmitter output plus the
re-reflected power. When this combo hits the load, the same percentage
is absorbed by the load as that extracted when the first power out of
the transmitter arrived at the load. The difference is that the incident
power is now greater as it has grown by the amount of the reflected
power. The re-reflected power is coming around again for another go at
the load.

Best regards, Richard Harrison, KB5WZI