The MPEC shows C/2022 E3 ZTF with e > 1.0.
[C/2022 E3 (ZTF)
Epoch 2023 Feb. 25.0 TT = JDT 2460000.5
T 2023 Jan. 12.78452 TT Rudenko
q 1.1122515 (2000.0) P Q
z -0.0002985 Peri. 145.81519 -0.60064011 -0.07341108
+/-0.0000009 Node 302.55536 +0.33752577 +0.87940934
e 1.0003320 Incl. 109.16818 +0.72478122 -0.47037223
From 4589 observations 2021 July 10-2022 Dec. 8, mean residual 0".5. ]
We are the official body that deals with astrometric observations and orbits of minor planets (asteroids) and comets.
minorplanetcenter.net
e > 1.0 does not complete a closed orbit around the Sun. Others I see show e in the area of 0.999999.... with efforts to show a closed orbit around the Sun. Claiming this comet was around when Neanderthals ate the mammoths
are extrapolations that appear dubious to me
Edit: 0.9999... is a barycentric e, how accurate that is remains to be seen