Why not put that logic inside your view? Like this:
# Function Based View (FBV)
def my_view(request):
    reversed = request.GET.get('reverse', '')
    return render(request, 'template.html', locals())
# Class Based View (CBV)
class MyView(ListView):
    template_name = 'path/to/template.html'
    queryset = MyModel.objects.filter(...)
    context_object_name = 'my_obj'
    def get_context_data(self, **kwargs):
        context = super(MyView, self).get_context_data(**kwargs)
        context['reversed'] = self.request.GET.get('reverse', '')
        return context
Then do:
{% if reversed %}
    do somthing
{% endif %}
On the other hand, if you still want to do this kind of logic in your template then you should create your own filter like this:
from django import template
register = template.Library()    
def is_in_dict(d, key):
    return key in d
and use it like this:
{% load my_filters %}
{% if request.GET|is_in_dict:"reverse" %}
    do somthing
{% endif %}