  HESS J1731-347 is a shell-type supernova remnant emitting both TeV gamma rays
and non-thermal X-ray photons, spatially coincident with the radio SNR
G353.6-0.7. Hadronic and leptonic scenarios (or a blend of both) are discussed
in the literature to explain the TeV emission from the object. In 2011, a
$\gamma$-ray excess was also found in the neighborhood of the source (HESS
J1729-345). Here we present results of an updated analysis obtained with the
meanwhile available additional H.E.S.S. data. Beyond HESS J1731-347, the
analysis reveals the morphology of the emission of the adjacent TeV source HESS
J1729-345 and the emission in between the two sources in greater detail. The
results permit us to correlate the TeV emission outside of the SNR with
molecular gas tracers, and to confront the data with scenarios in which the TeV
emission outside the SNR is produced by escaping cosmic rays.
