If printf '%s' "$A" doesn't show any backslash then they're not there. You can check with curl https://mysite.com alone.
Maybe you were confused by the output of:
bash-5.0$ typeset -p A
declare -- A="\"Hello World\""
That's bash outputting shell code that could be used to define that $A variable. In the syntax of the shell language, the \ is there to escape the following " to tell the shell that that " is part of the data and not the closing quote.
It could also have output:
declare -- A='"Hello World"'
Which does just same (and is safer). Or A=\"Hello\ World\" or $'"Hello World"', etc which are other forms of quoting in the shell language syntax.
printf '%s' "$A"doesn't show backslashes, then they're not there. What's the output oftypeset -p A?