The motion of thin curved falling particles is ubiquitous in both nature and industry but is not yet widely examined. Here, we describe an experimental study on the dynamics of thin cylindrical shells resembling broken bottle fragments settling through quiescent fluid and homogeneous anisotropic turbulence. The particles have Archimedes numbers based on the mean descent velocity 0.75×104≲Ar≲2.75×1040.75×104≲Ar≲2.75×104. Turbulence reaching a Reynolds number of Reλ≈100Reλ≈100 is generated in a water tank using random jet arrays mounted in a coplanar configuration. After the flow becomes statistically stationary, a particle is released and its three-dimensional motion is recorded using two orthogonally positioned high-speed cameras. We propose a simple pendulum model that accurately captures the velocity fluctuations of the particles in still fluid and find that differences in the falling style might be explained by a closer alignment between the particle's pitch angle and its velocity vector. By comparing the trajectories under background turbulence with the quiescent fluid cases, we measure a decrease in the mean descent velocity in turbulence for the conditions tested. We also study the secondary motion of the particles and identify descent events that are unique to turbulence such as ‘long gliding’ and ‘rapid rotation’ events. Lastly, we show an increase in the radial dispersion of the particles under background turbulence and correlate the time scale of descent events with the local settling velocity.