The atmospheres of exoplanets are commonly studied by observing the transit of the planet passing in front of its parent star. The obscuration of part of the stellar disk during a transit will reveal aspects of its surface structure resulting from general centre-to-limb variations (CLVs). These become apparent when forming the ratio between the stellar light in and out of transit. These phenomena can be seen particularly clearly during the progress of a penumbral lunar eclipse, where the Earth transits the solar disk and masks different regions of the solar disk as the eclipse progresses. When inferring the properties of the planetary atmosphere, it is essential that this effect originating at the star is properly accounted for. Using the data observed from the 2014-April-15 lunar eclipse with the ESPaDOnS spectrograph mounted on the Canada France Hawaii Telescope (CFHT), we have obtained for the first time a time sequence of the penumbral spectra. These penumbral spectra enable us to study the centre-to-limb variations of solar Fraunhofer lines when the Earth is transiting Sun. The Na i and Ca ii absorption features reported from previous lunar eclipse observations are demonstrated to be CLV features, which dominate the corresponding line profiles and mask possible planetary signal. Detecting atmospheric species in exoplanets via transit spectroscopy must account for the CLV effect.