Pricing the Mass Sheet: External Convergence and the Size of the Correction the Hubble Constant Cannot Avoid

An unmodelled external convergence biases the Hubble constant inferred from time delays by the factor implied by the mass-sheet transformation. Using published per-system convergence estimates for the six H0LiCOW fields, with a sample mean of 0.0295 and root-mean-square 0.03, ignoring the correction entirely would bias the combined Hubble constant high by 2.16 km/s/Mpc. Reaching half-per-cent accuracy on the sample mean requires the mean convergence known to 0.005, which, at a realistic per-field uncertainty of 0.03, demands of order 36 independent fields, or per-field precision well beyond what galaxy-count methods currently deliver. The environment correction is therefore a first-rank term in the budget, not a refinement. Computed from published values; not measured.