You might want to keep the bedliner -- it will keep scratches, dents, etc.
from the bed.

If you need to attach tie-downs, here are two suggestions.

1.  Check out anyplace that sells tie-down hardware and trailer hitches --  
start at an auto parts store, also check out Lowe's or Home Depot -- they
sell trailer balls and the like.  What you are looking for is a tie-down
that fits into the stake holes on the edge of the bed.  Look at the edge
rail of the bed where you will find four rectangular holes, two up front,
two in the rear.  You can buy a thing that has a heavy chrome ring on top
with a chrome base -- there is a threaded shaft on the bottom of the chrome
ring with a wing nut on it -- just slip this into the hole and tighten it --  
instant tie-down.

Here are some examples:
http://www.prolineracks.com/bull-ring-anchors.html

Look at this one -- you can see the wingnuts:
http://www.brandsonsale.com/ht-001583-images.html

Look at the photos on this link:
http://www.schlatter.org/bubba_and_flash.htm
You'll see a chrome ring tie-down installed in the front two stake holes of
my truck.  I did not install tie-downs in the rear stake holes because I
used those holes to mount the antennas for my amateur radio equipment.

2.  Another possibility -- if you are certain where the stock tie-down hooks
are located on the bed, you could CAREFULLY cut holes in the bedliner to
gain access to the tie-downs.  When we bought my daughter a 2000 Ranger, we
had the dealer install a bedliner -- it came with holes already cut so we
have access to the tie-downs.

Hope this helps.

My opinion is to get rid of the thing. I always have, as they trap water and
junk and hasten the demise of your truck. I used to use the Rubbermaid style
mat that just sits in the back........I got rid of that for the same reason.
My solution?

Get a gallon of Herculiner brush on bed liner. It's about $50 on
sale......It will take you a week-end, but if you follow the directions,
it'll look great! For tie downs, I installed the flat style in holes in the
bed. Much easier to tie down stuff with hooks that fold flat when you don't
need them. Works great.

MM^^

The only way to go -  IMHO - is the spray on bed liner which
you can get many places or have it commercially done..  Had
an '06 F150 done a few months back for $240 south of
Atlanta.  Looks great, tough as nails and keeps things from
slidding around. You still have the use of any tiedowns that
may be there and does not trap debris or water under it to
wear away paint exposing metal to corrode.  The surface is
very hard and you will need to put a protective barrier of
some sort between it and things that scratch easily.  After
all, it is intended to protect the truck while you take care
of the cargo.

Lugnut

I bought some 1/8" plastic-coated metal cable from Home Depot, along with
some crimp-on cylinders (ferrules?).  Cut the cable in 2' lengths.  Make a
pass with the cable through the truck hooks and crimp the ends with the
ferrules.  Then you have something that you can hook into.  Very easy, very
durable.