Yes, remove the ivy ASAP! English ivy is a pest species pretty much everywhere and a noxious weed in many areas. And ivy allowed to grow on structures will hasten mold problems, rot and deterioration. There are scores of other, quite well-behaved groundcovers that would work for you and that aren't so agressive, invasive nor offer a home to vermine. Or expand your plant palatte and include other companion plantings - hostas, ferns, astilbe, etc. all thrive in the same conditions hydrangeas prefer.

Chisell, you may want to tactfully point out to the persistent BF that ivy doesn't twine or need support like clematis or some of the other vines because it adheres right to the structure - Ivy has tiny aerial rootlets that grow from the stems that will damage a wood surface over time. He's going to want to protect that deck investment :)