Long post, all reposts from other threads, hopefully its of use.
I'm assuming that by terrestrial you mean the medium and not the species. Algae/moss/whatnot are generally an issue with any moist/wet medium. The best option for keeping these to a minimum would be a light blocking sleeve for the glass unground part and a top layer of "dryer" medium. Both of these would reduce the overall growth of the Utric thou. I've been moving away from peat for years, I just don't feel its the right medium for CPs. I've had good luck with muds/sphagnum moss/tree fern/inorganic mediums and more recently seed starting sponges. With all I've learned in the last few years I just can not recommend peat/sand anymore, but I don't grow a lot of terrestrial Utrics anymore either.
Here are some old photos from U. quelchii growing in a setup I think a lot of Utrics would love. I have not had any algae issues yet with this setup, I believe the sphagnum is simply outcompeting the algae for nutrients. I've changed the water a time or two and I'll need to trim the sphagnum soon but the plant seems really happy with the arrangement. There is airflow down into the glass container part due to the sphagnum "top" but at the same time its very humid under the top. When you walk by all you need todo is take a quick look at the sphagnum and if its healthy its likely the Utric is also.
Utricularia quelchii by
randallsimpson, on Flickr
Utricularia quelchii by
randallsimpson, on Flickr
Utricularia quelchii by
randallsimpson, on Flickr
Utricularia quelchii by
randallsimpson, on Flickr
Utricularia graminifolia growing on some pond mud, currently this setup is algae/moss/whatnot infested. Atleast on the other side of the tank, the Utric will likely overrun and outcompete the algae/mosses overtime.
Utricularia graminifolia by
randallsimpson, on Flickr
Underwater side view.
Utricularia graminifolia by
randallsimpson, on Flickr
U. 'Jitka' in a jar with a tree fern totem/sphagnum moss top, water changed every 3-4 months I'd guess. Growing well and happy, mosses are an issue.
DSC_0335 by
randallsimpson, on Flickr
Another U. quelchii this one is a net pot inside a solo cup with some tree fern fibers + sphagnum moss. Water changed about once a year I'd guess. No issues at all so far. I have about 5 different species of Utrics growing in these cups. The newest ones are actually a short net pot filled with tree fern fibers inside a taller net pot with some sphagnum moss inside the solo cup with about 1/4-1/2" of water as a goal, but I don't watch them closely.
Utricularia quelchii by
randallsimpson, on Flickr
2.5g completely sealed up fish tank with Utric sandersonii and some random mediums, its been sealed for years. The "harvesting" tool was accidentally left in there, a very neglected setup. Mostly sphagnum moss is growing along with the Utric sandersonii.
DSC_0046 by
randallsimpson, on Flickr