Edward is discovering the limits of secret keeping. Lavender is right: Tedd will find out eventually, and if there are concerns about his learning certain things, better he learn it in a controlled environment from people he trusts, rather than at random out in the wild. Tedd’s reputation in the Uryom community, his mother, all that stuff is out there to jump at him from behind a bush (as his mother’s situation did when he was playing with the magic mirror, and as it nearly did when Nanase came face-to-face with one of Noriko’s old adversaries).
Edward needs to learn the difference between necessary and appropriate OPSEC and being overprotective of Tedd, who is their own person and able to make their own decisions.