As always, if you would show the code you used to create the table, it would make our job much easier...
The table command and friends (like array2table) have the named input parameter 'VariableNames' that you can use to create the names you wish on creation, or you can use the tableName.Properties.VariableNames property to assign the names after creation.
However, from the content of the table, it appears you did not use the "ReadVariableNames,1" parameter in order for whichever of the functions you did use that would have read the first record as variable names and given you those automagically.
Doing that would then let all the other data be treated as numeric and then being numbers, the apostrophes will go away.
The apostrophes are a display feature of MATLAB command window and cannot be removed from fields that are strings; they are the visual clue as to what type of variable is in the given column; a cellstr and char string variable are also shown as either in curly braces or single quotes. But, if you do the above and fix it to read the first record as variable names, then they will be seen as numeric and all will be well in the world.