Welp, the problem with the Tektro brakes is that they often come on bikes that need to have their mounts faced parallel with the wheel in order to get them setup real well, since they only have lateral adjustment.
The other thing to consider is properly setting the pad position, which (unfortunately) doesn't happen very often, since it takes a disproportionate amount of time when assembling the bike. In ideal conditions, you want a 1:2 ratio regarding the gap between the left pad and rotor:right pad and rotor. First things first, though...notice on the caliper that there is, on the right side, a large bolt with an opening for a 5mm hex key. This adjusts the placement of the fixed (right side) pad, which will become important soon.
The specific way I like to setup a mechanical disc is thus: 1st, make sure the wheel is firmly in the dropouts, and running true (placing the bike on the ground before closing the QR will ensure this). Next, using the 5mm hex key, make sure you have adjustment room with the right pad, enough to get about a 1mm gap between rotor and pad. To make sure the rotor and pads are parallel, first loosen the bolts attaching the caliper to the mount, then give the adjustment barrel for the cable a few turns, until the left pad is touching the rotor. Likewise, you will use the 5mm key to move the right pad until the caliper is locked on the rotor. It is crucial during this process that you make sure the caliper is still sitting squarely on the mount, and only moving laterally. Tighten the mounting bolts for the caliper, a bit at a time, alternating until both are at spec.
Now, back out the right pad a bit, and screw the barrel adjuster for the cable back in all the way. You should have a small gap between the left (moving) pad and the rotor, just enough for the wheel to spin freely. Using your hex key, you now want to adjust the right pad to the point where the gap is roughly twice as large as the left side.
This all will not make the brakes feel any better, but they will at least work better. As the pads wear, you will need to readjust the brake, using the barrel adjuster and pad adjusting bolt.