Templars are able to use their abilities. There's no mage to use something like Silence on—i.e., a Templar won't be able to just cut off/permanently stop whatever is going on—but cleansing the area of magic will cause things or beings that are not really there to flicker in and out of view for a moment before returning to normal. The Veil is very thin, so that's the most anyone will be able to do in terms of strengthening it.