Whether or not supernovae contribute significantly to the overall dust budget is a controversial subject. Submillimetre (submm) observations, sensitive to cold dust, have shown an excess at 450 and 850 microns in young remnants Cassiopeia A (Cas A) and Kepler. Some of the submm emission from Cas A has been shown to be contaminated by unrelated material along the line of sight. In this paper we explore the emission from material towards Kepler using submm continuum imaging and spectroscopic observations of atomic and molecular gas, via HI, 12CO (J=2-1) and 13CO (J=2-1). We detect weak CO emission (peak TA* = 0.2-1K, 1-2km/s fwhm) from diffuse, optically thin gas at the locations of some of the submm clumps. The contribution to the submm emission from foreground molecular and atomic clouds is negligible. The revised dust mass for Kepler's remnant is 0.1--1.2 solar masses, about half of the quoted values in the original study by Morgan et al. (2003), but still sufficient to explain the origin of dust at high redshifts. Comment: 12 pages, 9 figures, accepted to MNRAS