conservation of momentum is only a true, when translational invariance holds. In addition, there may be a countless number of mechanisms by which teleportation changes a persons momentum. E.g. maybe the way this kind of teleportation works is Star Tek-like and your atoms get disassembled and reassembled, meaning they don’t need to have the same overall momentum, when whatever is doing the dissassembly stops atoms for dissassembly.
People would just assume you lost a limb, which is not usually visible with your clothes on.