How do I get rid of this annoying tempo information in Write mode without deleting the playback?
View>Signpost, deselect (uncheck) Tempo
If these represent consistent slopes (i.e. getting faster or slower at a regular pace over the duration), perhaps you want to use the Line tool int he tempo editor, so instead of lots of immediate tempo changes one after another, you have a single gradual tempo change with just two points: one at the start and one at the end.
(And welcome to the forum @Elizabeth_Padrnos !)
Thank you for your answer.