You could make the variable VAR_A read only by adding a line:

readonly VAR_A

at the top of your script. This would cause the value of VAR_A to be preserved as per your local environment.

readonly: readonly [-aAf] [name[=value] ...] or readonly -p

Mark shell variables as unchangeable.

Mark each NAME as read-only; the values of these NAMEs may not be
changed by subsequent assignment.  If VALUE is supplied, assign VALUE
before marking as read-only.

Options:
  -a        refer to indexed array variables
  -A        refer to associative array variables
  -f        refer to shell functions
  -p        display a list of all readonly variables and functions

An argument of `--' disables further option processing.

Exit Status:
Returns success unless an invalid option is given or NAME is invalid.

You could make the variable VAR_A read only by adding a line:

readonly VAR_A

at the top of your script. This would cause the value of VAR_A to be preserved as per your local environment.

readonly: readonly [-aAf] [name[=value] ...] or readonly -p

Mark shell variables as unchangeable.

Mark each NAME as read-only; the values of these NAMEs may not be
changed by subsequent assignment.  If VALUE is supplied, assign VALUE
before marking as read-only.

Options:
  -a        refer to indexed array variables
  -A        refer to associative array variables
  -f        refer to shell functions
  -p        display a list of all readonly variables and functions

An argument of `--' disables further option processing.

Exit Status:
Returns success unless an invalid option is given or NAME is invalid.

The following example should make it clear:

$ export FOO="somevalue"        # environment variable FOO set to somevalue
$ cat test                      # test script
echo $FOO                       # print the value of FOO
readonly FOO                       # set FOO to local
FOO="something"                 # attempt to modify FOO
echo $FOO                       # print the value of FOO -- you would see the value that was inherited from the environment
$ bash test
somevalue
test: line 3: FOO: readonly variable
something