Stoat does the main work here: the Telegraph says the IPCC claimed that mountain ice has reduced over time but cited dodgy sources: a climbing magazine article and a dissertation about ice-climbing. Stoat notes that the claim (not claims) is a single line in a table that lists multiple observed effects to the cryosphere, and expressly focusses on the loss of ice climbs. Those two sources are actually pretty good sources for understanding ice climbs.
I'll add two other pieces of info that indicate the Telegraph doesn't know much about ice-climbing and apparently didn't seek out much information: first, it says that modern climbers wouldn't know if ice climbs from 100 years ago had disappeared. In fact, climbers are pretty good at tracking the history of climbing routes, especially first ascents. If a route used to exist 100 years ago and now is gone, there's an excellent chance that local climbers would know about it.
Second, the Telegraph says unnamed "experts" say "loss of ice climbs are a poor indicator of a reduction in mountain ice as climbers can knock ice down and damage ice falls with their axes and crampons." One would like to know who these experts are and exactly what they said. Yes it's true that climbers can damage and make unclimbable certain routes for a time period, but the ice will return each year unless global warming keeps that from happening.
Ice climbs typically follow waterfalls or cliff seeps that freeze up in the wintertime. There's no way that climber damage to ice in one winter will keep the climb from returning in the next winter. Actually a lot of ice should return multiple times in the same winter as the seeps and waterfalls continue to flow. Increased usage by ice climbers might increase the amount of time that a climb is unclimbable during a season, but it won't eliminate the route. Warming temps, on the other hand, can eliminate the ice permanently.
I'm not an ice-climber, by the way, I do snow and rock instead. But I know something of the sport and equipment and have seen it done. I think the Telegraph has got a few ice screws loose here in its effort to push a political viewpoint.