The laws regarding property and ownership can vary depending on your jurisdiction, so it's essential to consult with a legal professional for advice specific to your situation.
In many cases, the ownership of the washer and dryer would depend on who purchased the appliances or whose name is on the receipt or proof of purchase. If the appliances were purchased by your ex, they might have a legal claim to the items. However, this can vary depending on other factors, such as whether the appliances were gifted to you, if there was any agreement in writing about the property, or if there are any local laws that could apply.
If you are the rightful owner of the washer and dryer, and your ex has no legal claim to the appliances, you may not be obligated to allow them to pick up the items. You may want to communicate your position clearly and assert your rights to the appliances.
In some cases, if there is a dispute over ownership and it cannot be resolved amicably, a court order may be necessary to determine the rightful owner and settle the matter. This typically involves filing a lawsuit and presenting evidence in court to support your claim.
To fully understand your rights and obligations regarding the washer and dryer, it's crucial to consult with a qualified attorney who can provide legal advice based on the laws of your specific jurisdiction and the details of your situation.