One booking email may belong under both “Trip” and “Receipts”. In Gmail those labels can point to the same message; you do not need a second copy. Deleting the message, however, removes it from all its labels and the inbox. Choose the operation by what you want to keep.
Try it with one ordinary message
In Gmail on a computer, select a nonessential message, open Labels and apply two labels that you already use. Open each label and check that the same message appears. Note its sender, subject and date so that you can find it again without relying on a label.
To remove one association, select the message, open Labels and untick that label. Keep the other selected. Confirm that the message remains under the second label and can still be found by search. Do not use the trash button for this task.
Removing the label itself is a wider change
The More menu beside a label in the left sidebar has Remove label. That removes the organizing label, rather than just its association with one selected message. Decide which scope you intend before clicking.
With conversation view enabled, a manually applied label covers existing messages, not automatically every future reply. When a reply arrives, inspect it separately. An automatic filter is a different rule and should be tested on a small set before it handles future mail.