The issue is with the recipient's wallet. There is nothing that you can or need to do.
why I keep seeing this transaction as 'unspent'.
It is not saying the transaction is unspent. It is saying the output of that transaction is unspent, which is perfectly fine and expected. Bitcoin transactions use a system of spending and creating transaction outputs. If a transaction output is unspent, that means it is not spent by another transaction and indicates that the output is available to be spent. This means it is part of your wallet as your "balance".
In this case, you created a transaction which creates an output that is spendable by the recipient. Since the recipient has not spent the Bitcoin yet, the transaction output is unspent. That the recipient's wallet does not detect the transaction means that there is an issue with her wallet, not yours.