Lay My Hat

It's really not a worry. You've decided you don't want to do that.....so just advise that you don't offer that service however they are welcome to use the washing machine provided to launder the towels as often as they feel fit.

Also tell them you don't provide beach towels.

You're over thinking it.....which is easy to do in the early days (I know I did at times) that's why LMH is so valuable

Mousie
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+1
Wot Mousie, Sunbeam and others have said.
Guests have asked for something you don’t provide.
Very, very few properties would provide more than a weekly towel change so your position is entirely reasonable.
As your position is entirely reasonable, you have no reason to change it.
As changing your position for this one guest is not remotely practicable, don’t waste time considering it further.
You’ve provided everything they need - towels and washing facilities.
We all want to do our best for our guests; you have.
Use Mouse’s simple response.
...and relax.

This is slightly going against the grain, but could you offer to leave one spare set to help them with managing the washing/drying routine? I wouldn't normally suggest this but a three week booking is quite valuable.

Thank you to everyone who took the time to respond. It turns out the booking is for a party of 2, but the apartment is always made up for 4. I’ve politely explained that they will have double the normal amount and will be replaced with the same every Friday, so they can just swap them themselves mid-week and launder them if necessary.

I’ve had a reply: “OK, thanks.”

I think you’re all right, I’ve only been open a year, and still overthinking it, trying to make it all too perfect for everyone. We’ve not had any complaints yet from 25 bookings (apart from the wine glass shelf being too high, which we’ve altered), so I’m just going to leave them to get on with it.