Hans van der Meer schrieb am 07.06.2021 um 21:46:

In the following MWE for a textbackground the parameter backgroundoffset has the expected effect. But for positive values only. A backgroundoffset=-10pt has no visible effect.
But the real problem is the parameter frameoffset. No effect at all, whatever frameoffset= is set to.

The textbackground mechanism uses MetaPost to draw the background, lines etc.

Not all options are available for each background, e.g. frameoffset works by default only for side lines.

Wolfgang