$VAR1 = 'client_detail_admin_notes LIKE "%\\"quotes\\"%"';

Which obviously isn't right :(

Actually I think that is what you want. Remember that Data::Dumper doesn't exactly print the actual content of the variable, rather it prints code that may be used to instantiate it. So if you run:

$VAR1 = 'client_detail_admin_notes LIKE "%\\"quotes\\"%"';
print $VAR1;
[download]

you get:

as desired.