To repair the Workshop wall, you have to buy The Wall Repair Paint from the Store in the Varied Items section (be patient and wait till it appears over time).

Put the paint and brush beside the bucket on the lower right hand of the screen (near the sandbox). Drop someone on the bucket and they will proceed to fill the bucket with water and add the paint. They will then take it to the wall of the workshop (where the children draw on the wall) and they will proceed to paint the wall.

They will not complete the job on their own. You will have to keep bringing them back after they have finished one round. Use multiple people to finish the job quickly.

Note: Interrupting them while they are taking from the bucket will cause the bucket to disappear and all your progress on the wall will disappear too! You will have to wait for the Paint and brush to appear in the shop again.