In case anyone is interested, below is the latest map from the Mining Bureau. The concession that I circled is covered by 2 exploration licenses.
The first licence is called "Elek-Lökösháza - szénhidrogén" and is owned by "Magyar Horizont Energia Kereskedelmi és Szolgáltató Kft."
Szenhidrogen means "hydrocarbons"
The second license, covering exactly the same area, is called "Elek-Lökösháza - szénhidrogén (nem hagyományos)" and is owned by "Bekes Ventures Hungary Kft"
nem hagyomanyos means "non-conventional"
Obviously "Bekes Ventures Hungary KFT" will be the MOL/Exxon JV.