[Mark]

I need to make this transparent:

Outside of editing it by hand (since some of the lettering has no complete border), what's the best way?

I'm assuming you mean you would like the letters without background.

Anytime I have encountered a similar problem (border on a few of these letters), I have just cut out the letters with the pen tool. That would be my recommendation for this particular instance. I'll do it when I'm not on my laptop.