To "tailor" something is to make something specific to a given person or use. When you buy a "tailored suit", you are buying a suit that has been custom-made for you, as opposed to buying a suit off the rack at a department store. When a machine is "tailored" for a certain factory, that means that it has been modified to suit the particular needs of that factory.
So to "better tailor" something would be to do a better job of customizing it for a specific use or application. In context, to "better tailor the letter" would mean to edit the text in a way that makes it more suitable for a specific target audience or purpose.
As drɱ65 notes, the hypen is inappropriate here. It should be "to better tailor the letter", not "to better-tailor" it. "Tailor" is a verb that is being modified by the adverb "better". We do not use a hyphen in such a context. Perhaps the writer started out writing "this was a better-tailored letter", in which case the hyphen would be appropriate. You do use a hyphen to connect an adverb ("better") to an adjective that it modifies ("tailored").