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that would rot or have termites around here. at any rate you might be able to put some flashing or other metal corner guard on that spot to mitigate future damage. the gutter spout is usually pretty thin metal, you can probably put some leather gloves on and bend it back with your fingers pretty easily. is the flower bed delineated with anything like rocks or a low border fence? might think of doing that and ask for the area to be hand trimed/weeded or not touched at all and do it yourself.
I see a lot of dandelions, if you want those gone (they don't hurt anything) they will have to be sprayed, nobody commercial is going pull weeds in this day and age.
my son does landscaping occasionally and is right now outside weed wacking the whole yard. he will get room, board, and probably $100 for the couple hours he spends on the project. those machines are pretty powerful and it isn't hard to hit a few things if you aren't super careful. it takes real skill to do a good job, which means you have to pay a lot to get that kind of work done. people that balk at paying for labor often don't realize how much work "labor" really is. either you have to be present and supervise, or you have to pay the money for someone else to self-supervise (be skilled) or you pay to have a third party supervise.