I have a picture of the agreement to sell the tree to them for $1000 with my signature, dated, their letterhead, but no signature from them or specified amount of time?
You may have many things related to this alleged transaction.
What you don't possess is a valid contract.
Why not?
What Constitutes a Valid Contract?
An agreement becomes a contract binding IF it contains the following elements:
Mutual Assent: Each party must have a shared understanding regarding what the subject matter of the contract is. For example, for a delivery contract, both parties must understand that the word "ship" does not refer to a sea vessel, but rather means "to deliver".
Offer and Acceptance: One party must make an offer by clearly communicating their intent to be bound in a contract. Likewise, the other party must render their acceptance in unambiguous terms.
Consideration: Both parties mutually exchange something of value in order to make the agreement binding. The consideration may simply be a formality, such as giving $1. Sometimes contracts can be enforced in a one-sided promise where only one party renders consideration.
Your piece of paper lacks the consent/agreement and the signature of an authorized party able to contract on behalf of the corporation.
I suggest you find a buyer willing to fork over hard cash for your tree.
Promises aren't enforceable under our system of jurisprudence, as promises can never a contract make.
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As a practical matter
If the tree in question is the common variety Mexican Fan Palm, they usually do not have resale value because the labor required to remove the tree far outweighs the potential resale value of the tree.
How much does it cost to remove palm tree?
Palm tree removal costs depend on several different factors, but the most important indicator of price is typically the height.
As with trimming a palm tree, the height of the tree has a huge impact on how much it will cost to remove the tree :
Up to 30 Feet Tall = $150 to $450.
Between 30 and 60 Feet Tall = $200 to $950.