Typically what you want is for backspace to send ^? and not ^H. (I need a citation, but this is typically how modern terminals work.)
It looks like MobaXterm has an option to have backspace send ^H, I imagine that option is currently set on your MobaXterm, perhaps start by trying to uncheck that option.
Then you should look into why Vim has an impression ...
My understanding of the word job in that doc is that it refers to whatever is running in the :term (a shell, gdb, etc.).
You can encode the message in bash with printf:
printf '<Esc>]51;%s\a' message.
Here, the esc sequence is entered as Ctrl-V followed by Esc