We describe an update to the Herschel-Spectral and Photometric Imaging Receiver (SPIRE) Fourier-transform spectrometer (FTS) calibration for extended sources, which incorporates a correction for the frequency-dependent far-field feedhorn efficiency, eta(ff). This significant correction affects all FTS extended-source calibrated spectra in sparse or mapping mode, regardless of the spectral resolution. Line fluxes and continuum levels are underestimated by factors of 1.3-2 in thespectrometer long wavelength band (447-1018 GHz; 671-294 mu m) and 1.4-1.5 in the spectrometer short wavelength band (944-1568 GHz; 318-191 mu m). The correction was implemented in the FTS pipeline version 14.1 and has also been described in the SPIRE Handbook since 2017 February. Studies based on extended-source calibrated spectra produced prior to this pipeline version should be critically reconsidered using the current products available in the Herschel Science Archive. Once the extended-source calibrated spectra are corrected for eta(ff), the synthetic photometry and the broad-band intensities from SPIRE photometer maps agree within 2-4 per cent - similar levels to the comparison of point-source calibrated spectra and photometry from point-source calibrated maps. The two calibration schemes for the FTS are now self-consistent: the conversion between the corrected extended-source and point-source calibrated spectra can be achieved with the beam solid angle and a gain correction that accounts for the diffraction loss.