I'm calling powershell from cmd, and passing quotes and neither escapes here worked. The grave accent worked to escape double quotes on this Win 10 surface pro.
>powershell.exe "echo la`"" >> test
>type test
la"
Below are outputs I got for other characters to escape a double quote:
la\
la^
la
la~
Using another quote to escape a quote resulted in no quotes. As you can see, the characters themselves got typed, but didn't escape the double quotes.