Hi @jeanesco ,
You may wish to verify how old the speaker is first as JBL have a 1 year [https://www.jbl.com/support-warranty.html|manufacturer’s warranty] on the speaker.
If it is less than 1 year old and hopefully the gift donor still has the sales receipt or proof of purchase, follow the directions in the warranty as to what to do to make a claim for a manufacturer’s warranty repair or replacement.
If it is out of warranty or there is no sales receipt available anymore then here’s a link to the ifixit [guide|94789] guide.
This guide is not so much a replacement battery guide , rather a workaround to connect an external compatible battery to the speaker. Perhaps the guide was written before the correct replacements became available.
However, you can still use most of the guide to gain access to the battery for replacement with a suitable compatible internal battery.
Here’s a link to just one [https://www.ebay.com/sch/i.html?_from=R40&_trksid=m570.l1313&_nkw=jbl+extreme+battery&_sacat=0|supplier]. It is shown only to give you an idea of the cost of the part. There are other suppliers available that may suit you better. Just search online for ''JBL Xtreme battery'' to get results.