[Python] return header without quotes in aws lambda + remove header if empty

I'm trying to return a header from a lambda, it's returned as "<https://example.com/ab?offset=0&limit=0>; rel=\"next\"" instead of <https://example.com/ab?offset=0&limit=0>; rel="next".

And also when I don't return the header, I still see it as "". This is my cdk:

_api_gw.MethodResponse(status_code='200',
response_parameters={'method.response.header.Link': True})

integration_response = _api_gw.IntegrationResponse(
status_code='200',
response_parameters=response_integration_parameters,
response_templates={
'application/json': """
#set($inputRoot = $input.path('$'))

## Map headers only if exist ##
#set($link = $input.json('$.Link'))
#if($link != "")
#set($context.responseOverride.header.Link = $link)
#end

## Clean JSON body (exclude headers) ##
{
"data": $input.json('$.data'),

}
"""
}


default_request_template = {
"application/json": '{ "method": "$context.httpMethod", "body" : "$util.escapeJavaScript("$input.json(\'$\')")", "headers": { #foreach($param in $input.params().header.keySet()) "$param": "$util.escapeJavaScript($input.params().header.get($param))" #if($foreach.hasNext),#end #end }, "queryParams": { #foreach($param in $input.params().querystring.keySet()) "$param": "$util.escapeJavaScript($input.params().querystring.get($param))" #if($foreach.hasNext),#end #end }, "pathParams": { #foreach($param in $input.params().path.keySet()) "$param": "$util.escapeJavaScript($input.params().path.get($param))" #if($foreach.hasNext),#end #end }}'
}

resource.add_method('GET',
_api_gw.LambdaIntegration(
my_lambda,
proxy=False,
request_templates=default_request_template,
integration_responses=[
integration_response]),
method_responses=[
_api_gw.MethodResponse(status_code='200',
response_parameters={
'method.response.header.Link': True})])

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