verb
obtrude
uhb-TROOD/əbˈtruːd/
To force something or oneself into notice in an unwelcome way.
The promoter obtrudes the perfume bottle between the shopper and the handbag she is examining.

Etymology
Thrusting something forward becomes forcing it upon someone's attention. The same image applies when people push themselves into notice rather than remaining unobtrusive.
In context
don't let any other thought drift in just the moment one starts to obtrude make it get out
More examples
- I try not to obtrude on their private conversation.
- Memories of the argument keep obtruding on her thoughts.
- She resents having his advice obtruded upon her.
Forms
obtrude · obtrudes · obtruded · obtruding
obtrusive adjective — Noticeable in an unwelcome or intrusive way.