Chemical vapor deposition (CVD) is a powerful technique to produce graphene for large-scale applications. Polymer-assisted wet transfer is commonly used to move the graphene onto silicon substrates, but the resulting devices tend to exhibit p-doping, which decreases the device quality and reproducibility. In an effort to better understand the origin of this effect, we coated graphene with n-methyl-2-pyrrolidone (NMP) and hexamethyldisilazane (HMDS) molecules that exhibit negligible charge transfer to graphene but bind more strongly to graphene than ambient adsorbents. Using Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), electrical transport measurements, and quantum mechanical computer simulations, we show that the molecules help in the removal of p-doping, and our data indicate that the molecules do this by replacing ambient adsorbents (typically O2 and water) on the graphene surface. This very simple method of improving the electronic properties of CVD graphene by passivating its surface with common solvent molecules will accelerate the development of CVD graphene-based devices.