The fence in Waverley Park, Kirkintilloch, was seriously damaged in the blaze which took place at around 10pm on Thursday, July 19.
Meanwhile, a dog owner is facing a fine after failing to clean up after his pet.
The 41-year-old man was charged by police at around 9.30am on Monday, July 16, in Redbrae Road, Kirkintilloch.
The man was accused of taking £10-worth of items from the discount store in Cowgate at around 3.50pm on Sunday, July 22.
If you have any information about a crime, contact police on 0141 532 4400.