To delete a soil sample, go to Drawing Tools | Delete Features | Soil Samples. Click on the soil sample(s) you would like to delete.

A Delete Soil Samples box will pop up. Once you have selected all the soil samples you would like to delete click Delete Soil Sample.  

Another box will pop up asking if you're sure you would like to delete the selected soil sample(s). Click OK. The soil sample(s) selected will now be removed from the map.