This is bush honeysuckle, a foreign invasive shrub even more implicated in the spread of Lyme disease than barberry. In bush honeysuckle patches, the risk of ticks infected by Lyme is 10 times greater than normal. (It’s 8.8 times higher in barberry stands, though research suggests the cause of infected tick increase is different for the two shrub species.) By all means, cut down the honeysuckle shrub, especially before its innumerable berries appear and spread it further. Recut or spray any regrowth. Debris can be taken off site or left to decompose. Create wide paths through your wooded areas so you can safely walk without brushing against plants. When not in flower, bush honeysuckle is still fairly easy to identify by its opposite smooth-edged leaves. Send us photos of any other plants you need identified to determine whether they are native or should go.