This gesture can reinforce goodwill and potentially secure her tenancy for longer, which is invaluable.Alternatively, if the budget allows, you might consider replacing them yourself.

It's incredibly hard to transfer "good will".         

My biggest concern is how to structure it to maximize positive benefits and good will without sacrificing too much "control".

There is no sense in ruining goodwill over a trivial issue.

My family has some good will in the area.

Subsequently, after establishing a balanced relationship with the tenant, you can consider making upgrades to the landlord's apartment,as a sidenote: Should any usable items be removed during renovations, offering them to the tenant can foster goodwill and enhance the tenant-landlord relationship.

As for the neighbors, they appreciate that we took a neighborhood eyesore and made it the nicest house on the block so that goes a long way towards building goodwill. 

You can build up goodwill sending grocery cards at Christmas, having a mini fridge to rush over the moment there is a problem, giving rent credits, etc. and it will mean LESS THAN ZERO as soon as you have a late fee you expect them to pay, a pet that you cannot approve, anytime the rent goes up, telling them they can't paint the walls and ceiling the color they want... then you are the scumbag landlord.

@Aryan StraussSomehow, this just made me think of Ben Affleck’s line in the movie Good Will Hunting.

For a hands on investor it can be a goodwill gesture to bring blankets and water and check on your tenants and the property.