I believe your BTC trader is a fake. They are a confidence trickster. They are trying to confuse you. They will ask you to pay an extra fee, they will keep inventing fees until you realise they do nothing but take money.
For reference, all Bitcoin transactions are copied across the Bitcoin network and every computer in the network keeps a list of unconfirmed transactions. This list is often called the mempool. Every computer with normal Bitcoin software has its own mempool. All transactions go into the mempool until they are confirmed. This is an unimportant detail. Your fake trader is only mentioning it in order to confuse you.
If a genuine trader was negligent and specified a very low transaction fee, the transaction might take longer than normal to be confirmed. It is the trader's responsibility to take whatever action is needed. A genuine trader would not need to tell you about this and would not need to increase any fee you are paying - all withdrawal fees should be fixed in their terms and conditions and should never come as a surprise to their customers.
No genuine business ever need to initiate email communication with a customer for such matters.