Acquire an ObjectReader with ObjectMapper#readerFor(TypeReference) using a TypeReference describing the typed collection you want. Then use ObjectReader#readValue(JsonNode) to parse the JsonNode (presumably an ArrayNode).

For example, to get a List<String> out of a JSON array containing only JSON strings

CopyObjectMapper mapper = new ObjectMapper();
// example JsonNode
JsonNode arrayNode = mapper.createArrayNode().add("one").add("two");
// acquire reader for the right type
ObjectReader reader = mapper.readerFor(new TypeReference<List<String>>() {
});
// use it
List<String> list = reader.readValue(arrayNode);

Yes, the Jackson manual parser design is quite different from other libraries. In particular, you will notice that JsonNode has most of the functions that you would typically associate with array nodes from other APIs. As such, you do not need to cast to an ArrayNode to use. Here's an example:

JSON:

{
    "objects" : ["One", "Two", "Three"]
}

Code:

final String json = "{\"objects\" : [\"One\", \"Two\", \"Three\"]}";

final JsonNode arrNode = new ObjectMapper().readTree(json).get("objects");
if (arrNode.isArray()) {
    for (final JsonNode objNode : arrNode) {
        System.out.println(objNode);
    }
}

Output:

"One"
"Two"
"Three"

Note the use of isArray to verify that the node is actually an array before iterating. The check is not necessary if you are absolutely confident in your data structure, but it's available should you need it (and this is no different from most other JSON libraries).

Moving my comment to an answer, as it got upvoted a lot.

This should do what the OP needed:

new ObjectMapper().convertValue(jsonNode, ArrayList.class)

Have to get rid of the backslash in the string

No, you really don't.

so it might be treated as String.

It actually is, and the fact that you are viewing it as a String is the reason why the escape characters exist.

If you pass the response.get("value").toString() to an ObjectMapper parser, you should get back an array or list

How to use Jackson to deserialise an array of objects

List<String> values = MAPPER.readValue("[\"hello\", \"world\"]", new TypeReference<List<String>>(){});
System.out.println(values); // [hello, world]

The alternative, more preferred, solution is to fix the producer of the initial JSON.

ObjectMapper mapper = new ObjectMapper();
List<Employee> e = new ArrayList<Employee>();
ArrayNode array = mapper.valueToTree(e);
ObjectNode companyNode = mapper.valueToTree(company);
companyNode.putArray("Employee").addAll(array);
JsonNode result = mapper.createObjectNode().set("company", companyNode);