Using VLT/ISAAC, we have detected 2 candidate counterparts to the bursting pulsar \groj, one bright and one faint, both within the X-ray error circles found using XMM-Newton and Chandra. In determining the spectral types of the counterparts we applied 3 different extinction corrections; one for an all-sky value, one for a Galactic Bulge value and one for a local value. We find that the local value, with an extinction law of alpha = 3.23 +/- 0.01 is the only correction that results in colours and magnitudes for both the bright and faint counterparts that are consistent with a small range of spectral types, and in the case of the bright counterpart are also consistent with the spectroscopic identification. Photometry of the fainter candidate then indicates it is a K7/M0 V star at a distance of 3.75+/-1 kpc. Such a star would require a very low inclination angle (i<9o) to satisfy the mass-function constraints; however this source cannot be excluded as the counterpart without follow-up spectroscopy to detect emission signatures of accretion. Photometry and spectroscopy of the bright candidate indicate that it is most likely a G/K III star. The spectrum does not show \brg emission, a known indicator of accretion. The bright star's magnitudes are in agreement with the constraints placed on the probable counterpart by the calculations of \citetrapp97 for an evolved star that has had its envelope stripped. The mass-function indicates the most likely counterpart has M < 0.3 Mo for an inclination of i >= 15 DEGr; a stripped giant, or a main sequence M3+ V star would be consistent with this mass-function constraint. In both cases mass-transfer, if present, will be by wind-accretion as the counterpart will not fill its Roche lobe given the observed orbital period. In this case, the derived magnetic field strength of 2.4 * 1011 G is sufficient to inhibit accretion of captured material by the propeller effect, hence the quiescent state of the system.