Battery change Kia Venga

Hello together! I drive a Kia Venga, and the battery has broken. I ordered a new one from Varta, which fits according to the TSN/HSN number from the vehicle license, but it is significantly larger than the one that was installed before. Such sizes are only available on No-Name China batteries, which I would not like to order. An official Kia dealer requires for a battery three times what I paid for, and does not say which model is installed. The battery I ordered, could be installed theoretically, but it no longer fits into the fabric thermal protection cover that was with the old battery. Do I have to keep this cover or can I leave it out? Will the effect on the use of the battery have? Thanks for your help!