  Integrable integral operator can be studied by means of a matrix
Riemann--Hilbert problem. However, in the case of so-called integrable
operators with shifts, the associated Riemann--Hilbert problem becomes operator
valued and this complicates strongly the analysis. In this note, we show how to
circumvent, in a very simple way, the use of such a setting while still being
able to characterize the large-$x$ asymptotic behavior of the determinant
associated with the operator.
