@ Pandora Drak - Those posts look like friendly bumps and although they are close to the bump button timer limit, they do not actually exceed it. There currently is no rule breaking there that needs action from the F Mod team.
If you find the posts to be a bother or an annoyance, you are welcome to politely say something along the lines of "Thank you for the bumps. However, we'd prefer if you left any bumping to our clan members." If the posts continue after that, then we can take that as an indication that they are not so friendly and intervene.
I understand what you mean but they are 2 different accounts. I'm not sure the F-Mods can interject here as both accounts are owned by the same person and both trading for items.
I would need to send this to Jagex but I highly doubt anything can be done to stop it as a lot use this method to get around the trade thread limit.
Comprehensive Account Security