Einstein@Home - what is the purpose of "gamma pulsar binary search" tasks? I participate in Einstein@Home program.
My question is - what is the purpose of "gamma pulsar binary search" tasks?
What signatures are being searched?
How gamma pulsar binaries can help in study of GR and gravitational waves?

EDIT:
After some research I've summarized in a self-answer, but I'm not sure is it right or wrong.
 A: Self-research is everything :)
Now I have at least partial answer.
Gamma pulsar binaries are consisted of pulsar and normal star (usually very bright) rotating close enough to each other.
This paper tells about millisecond pulsar found by gamma ray pulsations analysis. But millisecond pulsars are of direct interest in GR. They are nearly-ideal clocks and so are used in IPTA observations. The observations are aimed to search low-frequency gravitational waves (from supermassive black hole pairs corotation and probably primordial waves from Big Bang).

(source)
So, if I understand correctly, gamma ray binary search helps to narrow down search space for millisecond pulsars. Actually not all pulsars found this way will be millisecond pulsars, but if some new of them are found in radio follow-up - it's good because it expands the database for pulsar timing observations.
This paper is about the signatures being searched in gamma rays (by Fermi LAT instrument). Gamma radiation is caused by interaction of stellar winds of pulsar and companion star. Gamma rays have periodic variations because of corotation of the components.
A: Pulsars provide rather accurate clocks.  For a binary system one (or both) member of which is a pulsar this means you can determine things about the orbit of the system by looking at periodic frequency shifts in the pulse train from the pulsar.  In particular you can work out the orbital period pretty easily, and I think using astrophysics magic you can also infer things about the masses of the objects concerned (I think this must depend on having models which tell you how massive pulsars are: once you know that you can infer the mass of the other object.)
Orbiting systems lose energy through gravitational radiation, according to GR: this is true for all systems but for very many of them GR is such a tiny correction to Newtonian gravity that the amount of energy lost is absurdly tiny: the Earth-Sun system, for instance, radiates about $200\,\mathrm{W}$ (if GR is correct: assume this caveat below) which is completely undetectable.
Systems of two massive stars in rather close orbits however, can lose significant energy through gravitational radiation, and the orbits of the systems decay as a result.  In the limiting case the two bodies spiral in to each other and we can now detect the radiation from the last few seconds of the lives of some such systems directly.  However long before this it is possible to indirectly detect the loss of energy by observing changes in the orbital period: as the objects slowly spiral in to each other the orbital period decreases.
So, if we can find binary star systems at least one member of which is a pulsar and which are in fairly close orbits (all such systems will, eventually, be in close orbits as they lose energy through gravitational radiation) then we can use pulsar to measure the orbital period and in particular to measure changes in the orbital period, which GR says should be decreasing as energy is lost and the systems slowly spiral in.  This provides an indirect observation of gravitational radiation: we can compute what GR says the energy loss should be & hence compute what it says the rate of change of the orbital period should be, and compare it with what it actually is.
Famously the Hulse-Taylor binary is such a system and has provided a beautiful test of GR: within observational error the orbit of the system is decaying exactly as GR predicts it should.  Hulse & Taylor won the Nobel prize for this discovery.  (This system is emitting over $7\times 10^{24}\,\mathrm{W}$ through gravitational radiation: the Solar system, as a whole (which, really, is the Sun-Jupiter system and some fairly small corrections), is radiating about $5\times 10^3\,\mathrm{W}$, so this is about $10^{21}$ times 'brighter' as a source of gravitational radiation.)
So, this explains why binary systems containing pulsars are interesting: they provide tests of GR's prediction of gravitational radiation in regimes where we can't detect the radiation directly (which is almost all regimes).  Why are gamma pulsars particularly interesting?  I believe the reason for this is that gamma radiation does a very good job of penetrating clouds of dust, gas and other crud which may surround these systems, especially if they are supernova remnants (ie the neutron star which is the pulsar is the remnant after a supernova which has spat out a lot of crud surrounding the system).  For systems like this you may have to average over a very long time to get accurate information at radio wavelengths, while at gamma wavelengths you can get good data much more quickly.
So that's why finding pulsar binaries, and particularly gamma pulsar binaries, is interesting as tests of GR.
