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Do we know that the problem/issue is? Just because a tree is close to something doesn't mean it can be blamed for issues with a building. Its the easy thing to assume (just because its there), so cut the tree down then realise its nothing do to with it...
I would be asking what the issue is, evidence its being caused by your tree roots.
@Pantsmaster - either way I would probs get someone to do some hard pruning on that and try and bring it back into shape.
How close is the tree to the garage, and how big is the tree (height/canopy)?
EDIT: now I have looked at further posts, and in particular the photo, I would be 90% certain that the tree is the problem.