Would I mail the house a letter and hope it gets forwarded to someone? 

The letter never came. 

how do i compete with people who are throwing thousands of dollars a week on direct mail when im only doing one letter a month?

Transfer tax gets paid at the time the deed is presented to the recorder's office.Did the Deed come with a cover letter?

I send letters in the mail saying "I can pay with cash, I can close quickly."

I never return their calls or letters and if they show up on site my crew has specific instructions to escort them off the property and do their assessment from the public sidewalk.  

While you're at it, ask if anyone needs a hand answering phones or writing direct mail letters, or doing anything.

If the contract has not stated for that the writer did not specify the letters should be sent out or that there is a contingency with literally going to the tenants you might have to wait until after closing to do with the tenant.

We have used letters, postcards, invitations... a little bit of everything.

I want to write up a letter thanking them for being tenants with me, and also hopefully giving them some additional info or something like that.