They do. The Tcs0 tetraquarks don't have quark-antiquark pairs however, you see from the article and figures, that the quark content is charm + anti-strange + up + anti-down, these can't annihilate because the quarks have different flavours. They can "annihilate" via the weak interactions though, which can connect quarks and anti-quarks of different flavours. For example the charm-antistrange part could decay via a W-boson to a positron and a neutrino. This is a much slower process however.

In the pentaquark, charm-anticharm annihilation can and will happen. The time for charm-anticharm annihilation is usually slower relative to light and strange hadronic interactions though. In part because the strength of strong interactions reduces at higher energies, and the charm quark is more massive and so the relevant energy scale for the decay is higher.

One charm-anticharm resonance, the J/psi(3097) is very long lived even though the quarks can annihilate. In many theoretical models of these things, its often treated as a stable particle.

The particles are very shortlived, so the brief answer is that they do.