From the facts you've posted, you've given adequate notice. Your tenant cannot deny you the right to make repairs to protect the dwelling -- especially if those repairs don't involve going inside the leased premises.
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I do not see any reason why you would not be able to clean the gutters. This is an outdoor repair and if you do not repair this, it could likely do more damage to the inside of the home as well as tenant's belongings. You have followed proper procedure and given 24 hours notice (36 hours, actually), and you are well within your rights to repair the gutters.
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In this situation you may certainly make the repair to the gutters. You gave proper notice and your not even going inside to make the repair.