There are no standard answers to why they come and maintain a home and then disappear again, but here are my opinions:

1) it's a routine and something they don't really have to think about what they are doing;
2) it's a good way to stay connected to their former life;
3) it's a good way to keep an eye on what you are doing; or
4) it could very well be guilt.

I wouldn't sit and try to analyze why he's there doing the usual house maintenance. I would be happy he's doing it and be sure to thank him. Now, if it gets to the point you don't want him there, then you will have to tell him and set your boundaries...but remember, if you tell him you don't want him mowing the grass, then you'll have to do it or hire someone.

Sit quietly, the answers will reveal themselves when you least expect them to.
The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.