while there is some complexity here, I will try to get you pointed in the right direction.
First, yes you will need PHP to determine if the check box/database was updated with the check.
The basics would be to add a column in the database for sold. I would make the default entry "0" and then if you were to check the box, it would update the database to be "1". In other words, 0 meaning not sold and 1 meaning sold.
In your page, say you have a picture of your house in a div.
Below that you can then add your if statement.
Use PHP to check if the value for sold in that row is 1. If it is equal to 1, then you generate a new div with your sold graphic in that.
Lastly, you will want to set the position of that div to relative and preferably to the exact dimensions of your image. You will need to then set the Z-Index attribute high (like 100) and then begin to position the div with negative margins to show up over top the house pic.
For example, to get over the bottom right corner, you may have to set it to margin-top: -120px; margin-left: 50px;. That's just an arbitrary example of how a picture that was say 100px high would be placed.