I just realized that Thri-Kreen Claws does not specify whether it is a weapon or implement attack. It simply lacks the keyword. Does it mean it is none of them and therefore no feats and proficiency bonuses apply?
Yes, exactly. The Thri-Kreen Claws power is based on the natural claws of your Thri-Keen, and thus is a natural attack, treated by the rules like hitting somebody with your fist (see page 219 of the PH for Unarmed attack under "Improvised Melee Weapons").
Being essentially unarmed, you get no weapon or implement bonus, thus no modifiers for proficiency or alteration. But as claws are obviously more efficient than fists, you get a +3/+6/+9 to your attack roll (built into the power), and deal higher damage than a fist does.