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You need to provide additional information to clarify your question. Is there something special about the portion of land on which the house is built? If this land portion does not serve a special purpose to the easement holder and they are willing to accept easement over other land portions instead, your friend may be able to negotiate a favorable resolution.
What do you mean by "the property lines are difficult to establish and could be contested?" Was the land trust aware of the home construction, but did not speak up till after the home was built? If so, your friend may be able to raise some affirmative defenses to a potential suit by the land trust.
Your friend should immediately consult his/her own attorney to help preserve any legal rights he/she may have.
I agree with Mr. Mashal. The law favors efficiency and if the encroachment was inadvertant and the easement can be re-jiggered to make the injured party whole, then tearing down the house is likely to be disfavored by the court.
Talk with an attorney. The best approach is to try an negotiate a remedy outside of a lawsuit process and an attorney will be invaluable.