Black Eggs On Nasturtiums . You can pick them off by hand, or let the blue tits eat them. Probably large white butterfly caterpillars. The most effective cabbage white caterpillar trap! from producefromthegarden.co.uk We have found that black fly and aphids have been attracted to them which has been good as they have kept them away from other plants. Blackfly ate my nasturtium (13 posts) add message | report. There are also some black aphids on one leaf, i have tried rinsing them off but they're not budging, does anyone.