I have an incoming transaction with insufficient fees to confirm it. It flits between LOCAL or UNCONFIRMED. It's currently 130vMb from the tip (Electrum) or 112vMb on Blockstream. I think it's slowly getting further from the tip and it's been like this for 10 days.
Zaguru have already explained why you are seeing such in your wallet.
Options in Electrum are to BROADCAST it or CPFP both of which I think are pointless or to DELETE it. I have no idea what deleting it does, would it return to sender, if so how long would that take? Then start again with appropriate fees?
If you delete the transaction does not mean that it has been deleted. You need to make a similar transaction of the same amount or higher than the previous amount that you sent, and you should also increase the transaction fee.
Sender could RBF it but I'm not sure if there's a difference in RBF a LOCAL only transaction or an UNCONFIRMED one. If deleting it returns the BTC to the sender perhaps that's a better option?
Deleting it will not return the BTC to the sender, because it will still be another node mempool, that can pick up the transaction again. Of course, the sender can use RBF or CPFP, as mentioned by the first two posters above.