Yeah, they will work with the Tektro brakes. The BL-R2000 are convertible between short pull and long pull, you want to set-up them with the cable in the position closer to the lever pivot.

Modern Shimano flat-bar brake levers use a rivet in the pivot, which means they start with a certain amount of slop, and will only get worse with time. Most Tektro levers use a bolt and nut at the pivot, which allows you to tighten up the pivot to reduce or eliminate excess slop in the lever, which makes the brake feel better. If you want the best possible levers that will work, look at nicer vintage levers such as Dia-Compe SS-5 or Shimano BL-MT63. Or splurge on some Paul Canti Levers.