Sometimes it's valuable to remember the Old Testament context to New Testament statements.
The author of Hebrews uses the expression "strangers and pilgrims on the earth" in the following text:
Hebrews 11:13
These all died in faith, not having received the promises, but having seen them afar off, and were persuaded of them, and embraced them, and confessed that they were strangers and pilgrims on the earth.
1 Peter 2:11-12
Dearly beloved, I beseech you as strangers and pilgrims, abstain from fleshly lusts, which war against the soul; having your conversation honest among the Gentiles: that, whereas they speak against you as evildoers, they may by your good works, which they shall behold, glorify God in the day of visitation.
Interestingly, even both Hebrews and Peter are not written by the same inspired man, both Hebrews and Peter are written to first-century Jewish believers. These believers can be expected to have in mind the Old Testament use of the stranger/pilgrim motif.
Where does this concept originate in the Old Testament? The corresponding Greek word for "pilgrim" is found first in Genesis.
Genesis 23:4
I am a stranger and a sojourner with you: give me a possession of a buryingplace with you, that I may bury my dead out of my sight.
The idea of pilgrim or sojourner is used a number of times in the Old Testament, particularly regarding Abraham and his descendants from the time when he first came to Canaan until the reentry into Canaan.
My reason for bringing this up is that while Abraham and his family were strangers and pilgrims in Canaan, there is a sense in which they were not on a journey to somewhere entirely different - just to Canaan 430 years later.
In the same way, it makes sense to realize that one picture of the New Heavens and New Earth in Scripture is of something new coming down from heaven after the world-ending fire destroys everything, even the oceans. Thus, we are strangers and pilgrims here on this planet, but that does not preclude the post-resurrection new heavens and new earth from on this same planet, rebuilt after the fire. I certainly don't think I would feel comfortable being dogmatic about that, but the idea is fascinating.