When I have fruit scraps, I feed them - same with veggie and meat scraps as well as other leftovers. I have a 'chicken bucket' (a bowl with a lid) that I keep in the refrigerator - when I am prepping food I take it out and put the scraps right into it, dump leftovers in there, etc - we take it out a few times a week to give to the birds.
Whether a handful a day would be too much would depend on how many birds you are feeding. One handful between two birds, for example = a lot of fruit per bird, but that same handful between 20 birds= a lot less per bird. My personal take on this is that all things are good in moderation - treats (fruit, scraps, scratch grains, etc) should be no more than 10% of a their daily intake. If you want to offer just fruit at any one time maybe you can do it 1-2 times a week rather than daily and balance out the rest of the week with offerings from other nutritional make-ups?