We have the same type of trampoline in our garden

You can ignore your neighbours comments, there is nothing she can do about the visual aspect of the trampoline.

Of course, if your children jump and scream and laugh at 0300 or during the holy midday quiet period on a Sunday then she has the right to complain that the kids are disturbing the peace.

But she cannot complain about what she thinks is an "ugly" trampoline. You can respond back and say you think it is pretty and beautiful :-)
Beauty is in the eye of the beholder, as they say...

As for legalities?
You, as a parent, have the obligation to make sure the trampoline is in good sound working order and your children or other children won't be hurt through your negligence (ie: if you didn't maintain the tramp or ignored a ripped mat etc)

Otherwise, it's your tramp on your property...