It seems to me like we never measure things _directly_. For example: To measure the temperature of something in everyday life, we use a tiny glass cylinder filled with some kind of liquid. The liquid expands or contracts, roughly linearly, because of the temperature exchange with its surroundings. We then compare the current level of the liquid to a little ruler inscribed in the cylinder, maybe the markings form a shape similar to "100°C". The photons that bounce off this little ruler into our eyes causes impulses in some neurons and so on and our brains compare the shape "100°C" to yet another reference point, boiling water. It's hardly direct¤, in any sense of the word.
If we measure gravitational waves by observing "ripples in background radiation"¤¤, isn't that kind of the same thing? I've seen several people here mention that it's not "measured directly" - does it mean something else in this case?
¤ If you stick your hand into the boiling water to measure its temperature, it's a bit more direct but not as accurate.
¤¤ I'm just a programmer, this is kind of how I understood it. :D
For example, temperature is defined as rate of change of entropy of a system as energy changes, while entropy itself is defined as some formula dependent on number of microstates. If someone measures this rate directly, it would be called a direct measurement. In practice though, you would rely on some derived phenomena, like expansion of mercury. If you understand expansion of mercury from some other independent theoretical ground, then after some rigor, the use of mercury can also be taken as direct measurement of temperature.
In current case, what we would really like to observe is change in space-time as gravitational wave propagates, just like you would want to see ripple in waters to confirm a water wave. There are experiments that are trying to do exactly that (the LIGO for example), but you can also measure something which is a derived phenomena, the polarization of photons of the cosmic microwave background (CMB) radiation. There are good theories connecting why gravitational waves would produces such an effect in CMB, so this can be a tool for indirect observation.
Again this does boils down to usage and what community considers direct vs indirect observation, but as a rule of thumb, experiments which measure a quantity from definition of the quantity itself are considered direct; they are termed indirect otherwise.
As far as I can see from the article (couldn't find the paper detailing the experiment), they observed an artifact that could have been caused by primordial gravitational waves. This is different from using a thermometer to measure temperature because we're not sure yet whether that is the only possibility (or our instruments are not sensitive/too sensitive, it's a different mechanism of inflation etc.), it's the best explanation, but we're not extremely sure yet. (Although as I say this it occurred to me that it's probably much more certain than before because of the discovery.)
The key takeaway here is that the inflationary model is almost certainly the right one and gravitational waves are almost certainly real.
(This is similar to the first Higgs Boson announcement, where we were almost certain it was the Higgs, but not sure enough to claim discovery; because we hadn't determined all the properties of the observed particle)
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
and the CMB measurements by BICEPS are indisputably indirect. Gravitational wave detectors
like the LISA proposal