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
If you have a sufficiently modern vim that has the +terminal feature, you can do :term cat somefile and you'll get a buffer with all the terminal codes interpreted.
This might work better on large files than e.g. Colorizer, which made my vim unusably slow when I let it loose on a 6000-line file.
This Windows 10 terminal issue is documented in Vim background color renders incorrectly. A workaround is to set the vi background color to one of 16 working colors.
In ~/.vimrc put:
highlight Normal ctermfg=black ctermbg=lightgrey
When in vim, this sets the text color to black and the background color to lightgrey.
Use :help cterm-colors in vim to see ...