There's a good philosophy of science argument to be made that there's no
precise and
discrete distinction between direct and indirect measurement. In our model of the universe, there are always multiple physical steps that link the phenomena under investigation to our conscious perception. Therefore, any conclusions we draw from a perception are conditional on our confidence in the entire causal chain performing reliably (e.g. a gravitational wave induces a B-mode in the CMB, which propagates as a photon to our detectors, which heats up a transition-edge sensor, which increases the resistivity of the circuit, which flips a bit in the flash memory, which is read out to a monitor, which emits photons to our eye, which change the nerves firing in our brain). "Direct" measurements, then, are just ones that rely on a
small number of
reliable inferences, while "indirect" measurements rely on a
large number of
less reliable inferences.
Nonetheless, in practice there is a rather clear distinction which declares "direct" measurements to be those that take place locally (in space) using well-characterized equipment that we can (importantly) manipulate, and which is conditional only on physical laws which are very strongly established. All other measurements are called "indirect", generally because they are observational (i.e. no manipulation of the experimental parameters), are conditional on tenuous ideas (i.e. naturalness arguments as indirect evidence for supersymmetry), and/or involve intermediary systems that are not well understood (e.g. galactic dynamics).
The classic example is dark matter detection. A detector built in your laboratory that produces clear evidence of a local interaction between the dark matter partice and the atoms composing the detector would be "direct detection". Seeing an anomalous excess of gamma rays from the center of the galaxy whose energy and distribution is consistent with some theories which predict dark matter annihilation would be "indirect detection".
Naturally, direct measurements have a much larger impact on your Bayesian credences than indirect ones. If someone says "I don't trust that indirect measurement" they mean "one or more steps in the inference chain which connects the phenomena to our perceptions is unreliable".
EDIT: Oh, it's worth replying more directly (ha!) to your comment by noting that both pulsar slow downs
https://en.wikipedia.org/wiki/Gravitational_wave#Using_pulsa...
and the CMB measurements by BICEPS are indisputably indirect. Gravitational wave detectors
https://en.wikipedia.org/wiki/Gravitational_wave_detector
like the LISA proposal
https://en.wikipedia.org/wiki/Laser_Interferometer_Space_Ant...
are direct.