When they reject it, refuse any further payment of rent and evict them on nonpayment terms?

If the DOT wasn't filed, it's an unsecured debt, perfection of the lien is required and a Recorder may reject recording stale documents.   

It was listed for $220k, after extensive research I offered $130k (for poor area and about $30k in needed repair) my offer was rejected and 8 months later he accepted another offer for $130k.2) 4plex in South Hill Puyallup on 0.5 acres asking price $350k offered $355k.  

Once you get a few offers rejected you will realize that you will not be able to be so picky.I suggest you try to find some off-market deals, as those are usually the best bang for your buck. 

I have accepted offers from agents I know because they have been known to close and then I have rejected others because I know they are time wasters.

The realtor you choose needs to be ok with submitting tons of lowball offers and having most of them rejected which can be a lot of work for them.

Do I give them one and then send a reason for rejection?  

There have been few calls from realtors, One rejected offer, and only a few from internet sites.

Hi BPLong time investor, new agent.I have a handful of great investor clients.I find them deals, I even go out of my way.Property I find have great potential.I provide them with tools I wished my realtor gave me.I have Docusign for the offers they do.We put in offer.........I hit a huge wall.Offer rejected by agent before seller sees is.

If they have doubts about you, they reject your tactics.