J. Wilkinson Token

In this case, it increases the value. But there are some things to consider here:

1. Position of the engraving is good - no design is harmed (if this were the very rare variety with a window at the back of the shop then this would've effected the price)
2. The token isn't EF - its got good detail though. If it were EF, this would be considered damaging to the grade, but in this grade its not such a consideration and nobody would be going to buy it as a high grade example. Also important is that the token isn't worn slick.
3. Its rare to find these tokens engraved - its got a certain amount of novelty. I considered going for it because I've never seen another engraved Wilkinson.
4. The engraving is well executed, not haphazardly carved in with a paperclip.

It basically boils down to the fact that the host token is (very) common but the engraving is not. You're not going to find another in a hurry.

It would be worth even more if you have any idea who "JS" might have been. Unfortunately, the vast majority of "love tokens" have been long ago separated from the descendants of the original owner, stripped of provenance and therefore their historical context. Of course, it's always easier to confirm provenance if they'd carved more information than just initials.

In general, coin collectors still consider such items to be "damaged coins". We certainly don't want to be part of making it easy for anyone to "value add" their common tokens by adding artistic engravings onto them today.

Then there are modern owners wishing to give such items new meaning. I personally wouldn't want to pay extra for an engraved (vandalized) token, but I have a friend with initials "JS"; I've been looking for a nice original love token to give them. I would therefore pay extra for a carved token with these specific initials.