We are encouraged to receive out of compassion for those who want to give but we don’t “have to” receive everything that is offered, we are not obliged to receive anything at all.
Contentment is a virtue to be encouraged in monastics, but this has to be balanced with the virtue of giving, which should be encouraged in lay people! So, often at big events like a kathina ceremony we will just receive everything that is offered and anything that is surplus to requirements will be disposed of discreetly later, usually to charities.
However, if we don’t need something or don’t want it, we can politely refuse it. This has to be done carefully as it’s unskilful to shut down someone’s inspiration to give and might prevent them practicing generosity or offering in future.
Usually it’s good to ask what is needed and support that, rather than showing up with something that might not be wanted. Or offer an invitation for a particular thing, the monastics can take you up on it or not, or give an open invitation where they can tell you if they need something. This is good because sometimes we get caught up in what we want or what when we want, doing whatwe think is best, rather than giving what is needed when it’s needed.
One thing to consider also is that monasteries and temples can become quite ‘overrun’ with the kindness of laypeople, often the same things are offered repeatedly, which can create piles of stuff cluttering up the spaces, not only with small requisites but larger objects, too, like tables statues, caravans, potplant stands, garden sculptures, grandma’s old sofa and other random things! Often it’s well intentioned but it can become awkward if it’s not needed and then it disappears, upsetting the donor perhaps. We may have experienced something similar when someone who regularly visits our house gives something quite unwanted… awkward… Monasteries are semi public spaces, but are run by the monastics, so it’s fine for them to decide what stays and goes. Sometimes people can be quite pushy about offering things. I remember one person who kept on bringing old microwaves for some reason and getting upset that they weren’t needed because the monastery already had perfectly fine working ones.
In some situations where people are giving giving giving to the point that they might disadvantage themself there is a provision in the Vinaya to not approach them, so that they won’t end up destitute. On a lesser scale it’s wise to not rely on only a few people greatly, thus becoming a burden.
There is one last thing to mention, the practice of ‘overturning the bowl’ which is when monastics decide as a group to not receive offerings from people who have caused trouble in the community or who have been promoting wrong views etc. This is not a punishment per se but more a way of censuring - the Sangha still has a moral compass.
In your situation perhaps the monk doesn’t want to repair the Kuti for some reason, or doesn’t think it needs repairs. You can have a chat with them about it if you like and ask why or just accept that it’s not wanted currently. You can ask if there is something else that is needed if you’re still feeling generous. In your example of a blanket, it would seem a bit churlish to reject it, unless there was simply no room to store it.
It’s always good to give, some monasteries are well supported but others are not, so maybe give to them! There are plenty of worthy places and causes to give to outside of the Sangha, also.