By "Removal" all that is meant is that Joseph Anslow left his membership at Brewood Independent when he moved to Tipton. This is not to be confused with the poor law system of removal which was a forced removal of poor individuals to their home parish. On a previous page there is someone who removed "To America". This is also not a record of legal settlement, as non-conformist churches had no role in parish administration.
There is still a possibility that Anslow was removed under the poor law system. If so, you might find a removal order at a local archive, but survival of these records is often poor. Searches of the Staffordshire Archives and Black Country History catalogues doesn't bring up anything particularly promising.
Unless the chapel Anslow joined kept some sort of membership list like this one you have found for Brewood Independent Chapel, there is probably no further record of the event. There was an Independent Chapel at Union Street, Tipton, but I can't see any records for this chapel in TNA Non-conformist records. There were a plethora of other nonconformist churches at Tipton:
In various parts of the parish are no fewer than 15 dissenting places of worship.
There are five Wesleyan Methodist Chapels at Dudley Port, Great Bridge, Bloomfield, Lower-Green, and Gospel Oak.
The New Connexion Methodists have two chapels, at Dudley Port and Canal Street.
The Primitive Methodists have four chapels at Toll-End, Dudley Port, Chapel Street, and Waterloo Street.
There are two Baptist Chapels at Princes End and Toll-End, one Independent Chapel in Union Street, and one Unitarian Chapel in Waterloo Street.
Source: GENUKI: Tipton, Staffs
Chapels were certainly not mandated to keep a register of their members. Consider yourself lucky that you found one record that includes the date of his move!
There are a number of other types of records you could explore to determine how long Anslow stayed in Tipton. For example, he may appear on electoral rolls, trade directories, or tax lists if he lived there for some time. If he had children or family baptised, married, or buried at Tipton, you might be able to better establish how long he was at Tipton before moving just over the county border to Wellington, Shropshire.